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The roots of the equation $3{\mathrm{x}}^2-2\mathrm{x}+3=0$ are 
1.  real and distinct.
2.  real and equal.
3.  imaginary.
4.  irrational and distinct.

Find the sum and the product of the roots of the equation $\sqrt{3}{x}^2+27x+5\sqrt{3}=0.$
1.  $-9\sqrt{3}, 5$
2.  $9\sqrt{3}, 5$
3.  $6\sqrt{3}, -5$
4.  $6\sqrt{3}, 5$

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ are the roots of the equation ${\mathrm{x}}^2-12\mathrm{x}+32=0,$ then find the value of $\frac{{\mathrm{\alpha }}^2+{\mathrm{\beta }}^2}{\mathrm{\alpha }+\mathrm{\beta }}.$
1.  $\frac{-8}{3}$
2.  $\frac{8}{3}$
3.  $\frac{-20}{3}$
4.  $\frac{20}{3}$

Find the maximum or minimum value of the quadratic expression, ${\mathrm{x}}^2-3\mathrm{x}+5$ whichever exists.
1.  The minimum value is $\frac{9}{10}.$
2.  The minimum value is $\frac{11}{4}.$
3.  The maximum value is $\frac{9}{10}.$
4.  The maximum value is $\frac{11}{4}.$

Find the values of x which satisfy the equation, $\sqrt{3\mathrm{x}+7}-\sqrt{2\mathrm{x}+3}=1.$
1.  2, -2
2.  4, 3
3.  5, -1
4.  3, -1

If one of the roots of a quadratic equation having rational coefficients is $\sqrt{7}-4,$ then the quadratic equation is __________.
1.  ${\mathrm{x}}^2-2\sqrt{7}\mathrm{x}-9=0.$
2.  ${\mathrm{x}}^2-8\mathrm{x}+9=0.$
3.  ${\mathrm{x}}^2+8\mathrm{x}+9=0.$
4.  ${\mathrm{x}}^2-2\sqrt{7}\mathrm{x}+9=0.$

If the quadratic equation ${\mathrm{px}}^2+\mathrm{qx}-\mathrm{r}=0 \left(\mathrm{p}\ne 0\right)$ is to be solved by the graphical method, then which of the following graphs have to be drawn?
1.  $\mathrm{y}={\mathrm{x}}^2, \mathrm{y}=\mathrm{r}-\mathrm{qx}$
2.  $\mathrm{y}={\mathrm{px}}^2, \mathrm{y}=\mathrm{qx}-\mathrm{r}$
3.  $\mathrm{y}={\mathrm{x}}^2, \mathrm{qx}+\mathrm{py}-\mathrm{r}=0$
4.  $\mathrm{y}={\mathrm{x}}^2, \mathrm{qx}-\mathrm{py}=\mathrm{r}$

If the roots of the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ are $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, then the quadratic equation whose roots are $-\mathrm{\alpha } \mathrm{and} -\mathrm{\beta }$ is ____________.
1.  ${\mathrm{ax}}^2-\mathrm{bx}-\mathrm{c}=0$
2.  ${\mathrm{ax}}^2-\mathrm{bx}+\mathrm{c}=0$
3.  ${\mathrm{ax}}^2+\mathrm{bx}-\mathrm{c}=0$
4.  ${\mathrm{ax}}^2-\mathrm{bx}+2\mathrm{c}=0$

Find the sum and the product of the roots of the equation $-{\mathrm{x}}^2-\frac{25}{3}\mathrm{x}+25=0.$
1.  $\frac{25}{3}, 25$
2.  $\frac{-25}{3}, 25$
3.  $\frac{25}{3}, -25$
4.  $\frac{-25}{3}, -25$

For what value of k, if one root of the quadratic equation $9{\mathrm{x}}^2-18\mathrm{x}+\mathrm{k}=0$ is double of the other?
1.  36
2.  9
3.  12
4.  8

The sum of a number and its square is greater than 6, then the number belongs to ____________.
1.  $\left(-\infty , 2\right)\cup \left(3, \infty \right)$
2.  $\left(-\infty , -3\right)\cup \left(2, \infty \right)$
3.  (2, 3)
4.  [2, 3]

For which of the following intervals of x is ${\mathrm{x}}^2>\frac{1}{{\mathrm{x}}^2}?$
1.  $\left(-\infty , -1\right)\left(1, \infty \right)$
2.  $\left(-\infty , -1\right)\cup \left(1, \infty \right)$
3.  (-1, 1)
4.  [-1, 1]

If x and y are two successive multiples of 2 and their product is less than 35, then find the range of x.
1.  {2, 4, 0}
2.  {-6, -4, -2, 2, 4, 6}
3.  {-6, -4, -2, 0, 2, 4}
4.  {-6, -4, -2, 0, 2, 4, 6}

If ${\mathrm{x}}^3<\mathrm{n}, \mathrm{and} \mathrm{n}\in \left(-\infty , 0\right),$ then x
1.  is any real number
2.  is only positive number.
3.  has no value.
4.  is any negative number.

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ are the zeroes of the quadratic polynomial ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$ such that x does not lie between $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, then
1.  $\mathrm{a}>0 \mathrm{and} {\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}<0.$
2.  ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}<0 \mathrm{and} \mathrm{a}<0.$
3.  $\mathrm{a}>0 \mathrm{and} {\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}>0.$
4.  Both (2) and (3).

The condition for the sum and the product of the roots of the quadratic equation ${\mathrm{ax}}^2-\mathrm{bx}+\mathrm{c}=0$ to be equal, is ________.
1.  $\mathrm{b}+\mathrm{c}=0$
2.  $\mathrm{b}-\mathrm{c}=0$
3.  $\mathrm{a}+\mathrm{c}=0$
4.  $\mathrm{a}+\mathrm{b}+\mathrm{c}=0$

The quadratic equation having rational coefficients and one of the roots as $4+\sqrt{15},$ is __________.
1.  ${\mathrm{x}}^2-8\mathrm{x}+1=0$
2.  ${\mathrm{x}}^2+\mathrm{x}-8=0$
3.  ${\mathrm{x}}^2-\mathrm{x}+8=0$
4.  ${\mathrm{x}}^2+8\mathrm{x}+8=0$

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ are the zeros of the quadratic polynomial ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c} \mathrm{and} \mathrm{x}$ lies between $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, then which of the following is true?
1.  $\mathrm{If} \mathrm{a}<0 \mathrm{then} {\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}>0$.
2.  $\mathrm{If} \mathrm{a}>0 \mathrm{then} {\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}<0$.
3.  $\mathrm{If} \mathrm{a}>0 \mathrm{then} {\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}>0.$
4.  Both (1) and (2).

Find the nature of the roots of the equation $4{\mathrm{x}}^2-2x-1=0$.
1.  Real and equal
2.  Rational and unequal
3.  Irrational and unequal
4.  Imaginary

The solution of the inequation, $15{\mathrm{x}}^2-31\mathrm{x}+14<0$ is given by ___________.
1.  $\mathrm{x}\in \left(\frac{7}{5}, \infty \right)$
2.  $\frac{2}{3}<x<\frac{7}{5}$
3.  $\mathrm{x}\in \left(-\frac{7}{5},\infty \right)$
4.  $\mathrm{x}\in \mathrm{R}$

If ${\mathrm{mx}}^2<\mathrm{nx}$ such that m and n have opposite signs, then which of the following can be true?
1.  $\mathrm{x}\in \left(\frac{\mathrm{n}}{\mathrm{m}}, \infty \right)$
2.  $\mathrm{x}\in \left(-\infty , \frac{\mathrm{n}}{\mathrm{m}}\right)$
3.  $\mathrm{x}\in \left(\frac{\mathrm{n}}{\mathrm{m}}, 0\right)$
4.  None of these

Find the range of values of x which satisfy the inequation, ${\left(\mathrm{x}+1\right)}^2+{\left(x-1\right)}^2<6.$
1.  $\left(-\sqrt{2}, \sqrt{2}\right)$
2.  $\left(-1, 1\right)$
3.  $\left(-\infty , -2\right)\cup \left(2, \infty \right)$
4.  $\left(-\infty , -1\right)\cup \left(1, \infty \right)$

If the sum of the squares of three consecutive odd natural is 155, then their product will be equal to _________.
1.  99
2.  105
3.  693
4.  315

If ${\mathrm{x}}^2>0$, then find the range of the values that x can take.
1.  $\mathrm{x}=0$
2.  $\mathrm{x}\in \mathrm{R}$
3.  $\mathrm{x}\in \left(0, \infty \right)$
4.  $\mathrm{x}\in \mathrm{R}-\left\{0\right\}$

Find the range of the values of x which satisfy the inequation, ${\mathrm{x}}^2-7\mathrm{x}+3<2\mathrm{x}+25.$
1.  $\left(-2, 11\right)$
2.  $\left(2, 11\right)$
3.  $\left(-\infty , -1\right)\cup \left(2, 11\right)$
4.  (-8, -2)$\cup$[11, $\infty$)

If A and B are the roots of the quadratic equation ${\mathrm{x}}^2-12\mathrm{x}+27=0,$ then ${\mathrm{A}}^3+{\mathrm{B}}^3$ is ___________.
1.  27
2.  729
3.  756
4.  64

By drawing which of the following graphs can the quadratic equation $4{\mathrm{x}}^2+6\mathrm{x}-5=0$ be solved by graphical method?
1.  $\mathrm{y}={\mathrm{x}}^2, 3\mathrm{x}-2\mathrm{y}-5=0$
2.  $\mathrm{y}=4{\mathrm{x}}^2, 6\mathrm{x}-2\mathrm{y}-5=0$
3.  $\mathrm{y}={\mathrm{x}}^2, 6\mathrm{x}-\mathrm{y}-5=0$
4.  $\mathrm{y}=2{\mathrm{x}}^2, 6\mathrm{x}+2\mathrm{y}-5=0$

If the quadratic equation $\left({\mathrm{a}}^2-{\mathrm{b}}^2\right){\mathrm{x}}^2+\left({\mathrm{b}}^2-{\mathrm{c}}^2\right)\mathrm{x}+\left({\mathrm{c}}^2-{\mathrm{a}}^2\right)=0$ has equal roots, then which of the following is true?
1.  ${\mathrm{b}}^2+{\mathrm{c}}^2={\mathrm{a}}^2$
2.  ${\mathrm{b}}^2+{\mathrm{c}}^2=2{\mathrm{a}}^2$
3.  ${\mathrm{b}}^2-{\mathrm{c}}^2=2{\mathrm{a}}^2$
4.  ${\mathrm{a}}^2={\mathrm{b}}^2+2{\mathrm{c}}^2$

Which of the following are the roots of the equation ${\left|\mathrm{x}\right|}^2+\left|x\right|-6=0?$
(A) 2                           (B) -2
(C) 3                           (D) -3
1.  Both (A) and (B)
2.  Both (C) and (D)
3.  Both (A) and (C)
4.  (A), (B), (C) and (D)

What are the values of x which satisfy the equation, $\sqrt{5\mathrm{x}-6}+\frac{1}{\sqrt{5\mathrm{x}-6}}=\frac{10}{3}?$
1.  $3$
2.  $4, \frac{11}{9}$
3.  $\frac{11}{9}$
4.  $3, \frac{11}{9}$

If the roots of the quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0 \mathrm{are} \mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, then the equation whose roots are ${\mathrm{a}}^2 \mathrm{and} {\mathrm{\beta }}^2$ is ____________.
1.  ${\mathrm{a}}^2{\mathrm{x}}^2-\left({\mathrm{b}}^2-2\mathrm{ac}\right)\mathrm{x}+{\mathrm{c}}^2=0$
2.  ${\mathrm{a}}^2{\mathrm{x}}^2+{\mathrm{b}}^2\mathrm{x}+{\mathrm{c}}^2=0$
3.  ${\mathrm{a}}^2{\mathrm{x}}^2+\left({\mathrm{b}}^2+2\mathrm{ac}\right)\mathrm{x}+{\mathrm{c}}^2=0$
4.  ${\mathrm{a}}^2{\mathrm{x}}^2-\left({\mathrm{b}}^2+2\mathrm{ac}\right)\mathrm{x}+{\mathrm{c}}^2=0$

If the roots of the equation $3{\mathrm{ax}}^2+2\mathrm{bx}+\mathrm{c}=0$ are in the ratio 2 : 3, then ________.
1.  8ac=25b
2.  8ac=9b²
3.  8b²=9ac
4.  8b²=25ac

Find the roots of the equation ${\mathrm{l}}^2\left({\mathrm{m}}^2-{\mathrm{n}}^2\right){\mathrm{x}}^2+{\mathrm{m}}^2\left({\mathrm{n}}^2-{\mathrm{l}}^2\right)\mathrm{x}+{\mathrm{n}}^2\left({\mathrm{l}}^2-{\mathrm{m}}^2\right)=0.$
1.  $1, \frac{{\mathrm{n}}^2\left({\mathrm{l}}^2-{\mathrm{m}}^2\right)}{{\mathrm{l}}^2\left({\mathrm{m}}^2-{\mathrm{n}}^2\right)}$
2.  $1, \frac{-{\mathrm{m}}^2\left({\mathrm{l}}^2-{\mathrm{n}}^2\right)}{{\mathrm{l}}^2\left({\mathrm{m}}^2-{\mathrm{n}}^2\right)}$
3.  $1, \frac{{\mathrm{n}}^2\left({\mathrm{l}}^2+{\mathrm{m}}^2\right)}{{\mathrm{l}}^2\left({\mathrm{m}}^2-{\mathrm{n}}^2\right)}$
4.  $1, \frac{-{\mathrm{m}}^2\left({\mathrm{l}}^2+{\mathrm{n}}^2\right)}{{\mathrm{l}}^2\left({\mathrm{m}}^2-{\mathrm{n}}^2\right)}$

Comment on the sign of the quadratic expression ${\mathrm{x}}^2-5\mathrm{x}+6$ for all $\mathrm{x}\in \mathrm{R}.$
1.  ${\mathrm{x}}^2-5\mathrm{x}+6\ge 0 \mathrm{when} 2\le \mathrm{x}\le 3 \mathrm{and} {\mathrm{x}}^2-5\mathrm{x}+6<0 \mathrm{when} \mathrm{x}<2 \mathrm{or} \mathrm{x}>3.$
2.  ${\mathrm{x}}^2-5\mathrm{x}+6\le 0 \mathrm{when} 2\le \mathrm{x}\le 3 \mathrm{and} {\mathrm{x}}^2-5\mathrm{x}+6>0 \mathrm{when} \mathrm{x}<2 \mathrm{or} \mathrm{x}>3.$
3.  ${\mathrm{x}}^2-5\mathrm{x}+6\le 0 \mathrm{when} -1\le \mathrm{x}\le 6 \mathrm{and} {\mathrm{x}}^2-5\mathrm{x}+6>0 \mathrm{when} \mathrm{x}<-1 \mathrm{or} \mathrm{x}>6.$
4.  ${\mathrm{x}}^2-5\mathrm{x}+6\ge 0 \mathrm{when} -1\le \mathrm{x}\le 6 \mathrm{and} {\mathrm{x}}^2-5\mathrm{x}+6<0 \mathrm{when} \mathrm{x}<-1 \mathrm{or} \mathrm{x}>6.$

If $\mathrm{a}-\mathrm{b}, \mathrm{b}-\mathrm{c}$ are the roots of ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,$ then find the value of $\frac{\left(\mathrm{a}-\mathrm{b}\right)\left(\mathrm{b}-\mathrm{c}\right)}{\mathrm{c}-\mathrm{a}}.$
1.  $\frac{\mathrm{b}}{\mathrm{c}}$
2.  $\frac{\mathrm{c}}{\mathrm{b}}$
3.  $\frac{\mathrm{ab}}{\mathrm{c}}$
4.  $\frac{\mathrm{bc}}{\mathrm{a}}$

The values of x for which $\frac{\mathrm{x}+3}{{\mathrm{x}}^2-3\mathrm{x}-54}\ge 0$ are 
1.  $\left(-6, -3\right)\cup \left(9, \infty \right)$
2.  $\left[-6, -3\right]\cup \left[9, \infty \right]$
3.  $\left(-6, -3\right)\cup \left(-9, \infty \right)$
4.  $\left(-6, \infty \right)$

In a right triangle, the base is 3 units more than the height. If the area of the triangle is less than 20 sq.  units, then the possible values of the base lie in the region ________.
1.  (4, 6)
2.  (3, 8)
3.  (6, 8)
4.  (5, 8)

The value of x for which $-2\mathrm{x}-4\le {\left(\mathrm{x}+2\right)}^2 \le -2\mathrm{x}-1$ is satisfied are _____________.
1.  $\left[-5, -1\right]$
2.  $\left[-5, 0\right]$
3.  $\left[-5, -4\right]\cup \left[2, 1\right]$
4.  $\left[-5, -4\right]\cup \left[-2, -1\right]$

If $\frac{{\mathrm{x}}^2+\mathrm{x}-12}{{\mathrm{x}}^2-3\mathrm{x}+2}<0,$ then x lies in ___________.
1.  $\left(-4, 3\right)$
2.  $\left(-4, 2\right)$
3.  $\left[-4, -1\right]\cup \left[2, 3\right]$
4.  $\left(-4, 1\right)\cup \left(2, 3\right)$

For all real values of x, $\frac{{\mathrm{x}}^2-\left({\displaystyle \frac{\mathrm{x}}{2}}\right)+1}{{\mathrm{x}}^2+1}-\frac{5}{4}$ is ___________.
1.  equal to 1
2.  non-negative
3.  greater than $\frac{1}{4}$
4.  non-positive

If x² -4x + 3 > 0 and x² -6x + 8 < 0, then __________.
1.  x > 3
2.  x < 4
3.  3 < x < 4
4.  1 < X < 2

Find the product of the roots of ${\mathrm{x}}^2+8\mathrm{x}-16=0.$
1.  8
2.  -8
3.  16
4.  -16

If the roots of the equation $2{\mathrm{x}}^2+7\mathrm{x}=0$ are in the ratio P : q, then the value of $\sqrt{\frac{\mathrm{p}}{\mathrm{q}}}+\sqrt{\frac{\mathrm{q}}{\mathrm{p}}}.$
1.  $\pm \frac{7}{\sqrt{7}}$
2.  $\pm 7\sqrt{2}$
3.  $\pm \frac{7\sqrt{2}}{16}$
4.  $\pm \frac{7\sqrt{2}}{4}$

In a forest, a certain number of apes equal to the square of one-eight of the total number of their group are playing and having great fun. The rest of them are twelve in number and are on an adjoining hill. The echo of their shrieks from the hills frightens them. They come and join the apes in the forest and play with enthusiasm. What is the total number of apes in the forest?
1.  16
2.  48
3.  16 or 48
4.  64

If the roots of the quadratic equation ${\mathrm{x}}^2-2\mathrm{kx}+2{\mathrm{k}}^2-4=0$ are real, then the range of the values of k is ____________.
1.  $\left[-2, 2\right]$
2.  $\left[-\infty , -2\right]\cup \left[2, \infty \right]$
3.  $\left[0, 2\right]$
4.  None of these

Find the values of x for which the expression ${\mathrm{x}}^2-\left({\log }_{5}2+{\log }_{2}5\right)\mathrm{x}+1$ is always positive.
1.  $\mathrm{x}>{\log }_{2}5 \mathrm{or} \mathrm{x}<{\log }_{5}2$
2.  ${\log }_{5}2<\mathrm{x}<{\log }_{2}5$
3.  $-{\log }_{5}2<\mathrm{x}<{\log }_{2}5$
4.  $\mathrm{x}<-{\log }_{5}2 \mathrm{or} \mathrm{x}>{\log }_{2}5$

The roots of the equation x²-px+q=0 are consecutive integers. Find the discriminant of the equation.
1.  1
2.  2
3.  3
4.  4

Rohan and Sohan were attempting to solve the quadratic equation, ${\mathrm{x}}^2-\mathrm{ax}+\mathrm{b}=0.$ Rohan copied the coefficient of x wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3. Find the correct roots.
1.  -2 and -24
2.  2 and 24
3.  4 and 12
4.  -4 and -12

If (x+2)(x+4)(x+6)(x+8)=945 and x is an integer, then find x.
1.  -1 or -11
2.  1 or -11
3.  -1 or 11
4.  1 or 11

The difference of the roots of $2{\mathrm{y}}^2-\mathrm{ky}+16=0 \mathrm{is} \frac{1}{3}.$ Find k.
1.  $\pm \frac{32}{3}$
2.  $\pm \frac{34}{3}$
3.  $\pm \frac{38}{3}$
4.  $\pm \frac{40}{3}$

Find the condition to be satisfied by the coefficients of the equation px²+qx+r=0, so that the roots are in the ratio 3 : 4.
1.  12q²=49pr
2.  12q²=$-$49pr
3.  49q²=12pr
4.  49q²=$-$12pr

If the roots of the equation $3{\mathrm{x}}^2+9\mathrm{x}+2=0$ are in the ratio m : n, then find $\sqrt{\frac{\mathrm{m}}{\mathrm{n}}}+\sqrt{\frac{\mathrm{n}}{\mathrm{m}}}.$
1.  $\frac{-3\sqrt{3}}{\sqrt{2}}$
2.  $\frac{3\sqrt{2}}{2}$
3.  $\frac{3\sqrt{3}}{\sqrt{2}}$
4.  $\frac{-3\sqrt{3}}{2}$

If $\left({\mathrm{p}}^2-{\mathrm{q}}^2\right){\mathrm{x}}^2+\left({\mathrm{q}}^2-{\mathrm{r}}^2\right)\mathrm{x}+{\mathrm{r}}^2-{\mathrm{p}}^2=0 \mathrm{and} \left({\mathrm{p}}^2-{\mathrm{q}}^2\right){\mathrm{y}}^2+\left({\mathrm{r}}^2-{\mathrm{p}}^2\right)\mathrm{y}+{\mathrm{q}}^2-{\mathrm{r}}^2=0$ have a common root for all real values of p, q and r, then find the common root.
1.  -1
2.  1
3.  2
4.  -2

Which of the following are the roots of ${\left|\mathrm{y}\right|}^2-\left|y\right|-12=0?$
(A) 4                                 (B) -4
(C) 3                                 (D)-3
1.  Both (A) and (B)
2.  Both (C) and (D)
3.  Both (A) and (C)
4.  (A), (B), (C) and (D)

Find the value of $\sqrt{30+\sqrt{30+\sqrt{30+........\infty .}}}$
1.  6
2.  -5
3.  Either (1) or (2)
4.  Neither (1) nor (2)

If ${\mathrm{y}}^2+6\mathrm{y}-3\mathrm{m}=0 \mathrm{and} {\mathrm{y}}^2-3\mathrm{y}+\mathrm{m}=0$ have a common root, then find the possible values of m.
1.  $0, -\frac{27}{16}$
2.  $0, -\frac{81}{16}$
3.  $0, \frac{81}{16}$
4.  $0, \frac{27}{16}$

The students of a class contributed for a programme. Each student contributed the same amount. Had there been 15 more students in the class and each student had contributed ₹40 less, the total amount contributed would have increased from ₹3000 to ₹3200. Find the strength of the class.
1.  25
2.  15
3.  10
4.  20

The graph of $\mathrm{y}=2{\mathrm{x}}^2 \mathrm{and} \mathrm{y}=\mathrm{ax}+\mathrm{b}$ interest at two points (2, 8) and (6, 72). Find the quadratic equation in x whose roots are $\mathrm{a}+2 \mathrm{and} \frac{\mathrm{b}}{4}-1.$
1.  ${\mathrm{x}}^2+11\mathrm{x}-126=0$
2.  ${\mathrm{x}}^2-11\mathrm{x}+126=0$
3.  ${\mathrm{x}}^2+11\mathrm{x}+126=0$
4.  ${\mathrm{x}}^2-11\mathrm{x}-126=0$

The equation $9{\mathrm{y}}^2\left(\mathrm{m}+3\right)+6\left(\mathrm{m}-3\right)\mathrm{y}+\left(\mathrm{m}+3\right)=0,$ where m is real, has real roots. Which of the following is true?
1.  m = 0
2.  m < 0
3.  Either (1) or (2)
4.  Neither (1) nor (2)

Find the values of y which satisfy the quadratic inequalities below ${\mathrm{y}}^2+5\mathrm{y}+4\le 0 \mathrm{and} {\mathrm{y}}^2-2\mathrm{y}-15\ge 0.$
1.  $-1\le \mathrm{y}\le 5$
2.  $-4\le \mathrm{y}\le -3$
3.  $-1\ge \mathrm{y}\ge 5$
4.  $-4\ge \mathrm{y}\ge -3$

If $\frac{{\mathrm{y}}^2+\mathrm{y}-6}{{\mathrm{y}}^2+\mathrm{y}-2}<0,$ then which of the following is true?
1.  1 < y < 2
2.  -3 < y < -2
3.  Either (1) or (2)
4.  Neither (1) nor (2)

The product of two consecutive even numbers exceeds twice their sum by more than 20. Which of the following is the range of values that the smaller of the numbers can take?
1.  x>4 or x<-6
2.  -6<x<4
3.  x>6 or x<-4
4.  -4<x<6

Which of the following statements about the sign of the quadratic expression $\mathrm{E}={\mathrm{y}}^2-12\mathrm{y}+20$ is true?
1.  $\mathrm{E}\le 0 \mathrm{when} 20 \le \mathrm{y}\le 10 \mathrm{and} \mathrm{E}>0 \mathrm{when} \mathrm{y}<2 \mathrm{or} \mathrm{y}>10.$
2.  $\mathrm{E}\ge 0 \mathrm{when} 2 \le \mathrm{y}\le 10 \mathrm{and} \mathrm{E}<0 \mathrm{when} \mathrm{y}<2 \mathrm{or} \mathrm{y}>10.$
3.  $\mathrm{E}\le 0 \mathrm{when} -10 \le \mathrm{y}\le -2 \mathrm{and} \mathrm{E}>0 \mathrm{when} \mathrm{y}<-10 \mathrm{or} \mathrm{y}>-2.$
4.  $\mathrm{E}\ge -2 \mathrm{and} \mathrm{E} <0 \mathrm{when} \mathrm{y}<-10 \mathrm{or} \mathrm{y}>-2.$

If ${\left|\mathrm{y}\right|}^2-4\left|y\right|-60\le 0,$ then which of the following is the range of y?
1.  $\left[-6, 6\right]$
2.  $\left[0, 6\right]$
3.  $\left[0, 10\right]$
4.  $\left[-10, 10\right]$