GMAT Quadratic Equations

Question

The condition that a root of the equation ax^2 + bx + c = 0 may be reciprocal to a root of a_1x^2 + b_1x + c_1 = 0 is

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.
	E.

Question

The roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a) = 0 are real and equal if

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.
	E.

Question

If pr=2(q+s) then among the equations x^2 + px +q = 0 and x^2 + rx + s = 0

Possible Answers

Selected	Possible Answer
	A. At least one has real roots
	B. Both have real roots
	C. At least one has imaginary roots
	D. Both have imaginary roots
	E. None of these

Question

The roots of the equation $(a+c-b)x^2 + 2cx + (b+c-a) = 0\quad(a\not=b)$ are

Possible Answers

Selected	Possible Answer
	A. Real
	B. Real and distinct
	C. Imaginary
	D. Real and equal
	E. Equal

Question

If $\alpha,\beta$ are the roots of x^2 + ax - b = 0 and $\gamma,\delta$ are the roots of x^2 + ax + b = 0 , then the value of $(\alpha-\gamma)(\alpha-\delta)$ is

Possible Answers

Selected	Possible Answer
	A. -2b
	B. a+b
	C. a-b
	D. 2b
	E. 3b

Question

The harmonic mean of the roots of the equation , $(5+\sqrt{2})x^2 - (4+\sqrt{5})x + (8 + 2\sqrt{5}) = 0$ is

Possible Answers

Selected	Possible Answer
	A. 2
	B. 4
	C. 6
	D. 8
	E. 9

Question

The condition that the roots of $\frac{x-a}{ax+1} - \frac {x+b}{bx+1} = 0$ are reciprocal to each other is

Possible Answers

Selected	Possible Answer
	A. a+b=0
	B. b=0
	C. a-b=0
	D. a=0
	E. None of these

Question

If the equations 2x^2 + x + k = 0 and $x^2 + \frac{x}{2} - 1 = 0$ have common roots, then the value of is

Possible Answers

Selected	Possible Answer
	A. 1
	B. -2
	C. -1
	D. 3
	E. 4

Question

The expression (a-2)x^2 + 2(2a-3)x + (5a-6) is positive for all real values of , then

Possible Answers

Selected	Possible Answer
	A. a=3
	B. a>3
	C. a>1
	D. ‘a’ can be any real number
	E. a=1

Question

If is real and 5x^2 + 2x + 9 > 3x^2 + 10x + 7 , then lies in the interval

Possible Answers

Selected	Possible Answer
	A. $(-\infty , 2-\sqrt{3}) \cup (2+\sqrt{3},\infty)$
	B. $(2-\sqrt{1}, 2+\sqrt{1})$
	C. $(2-\sqrt{3}, 2+\sqrt{3})$
	D. $(2+\sqrt{3}, \infty)$
	E. None of these

Question

Find the maximum or minimum vale of the expression x^2 - 3x + 5

Possible Answers

Selected	Possible Answer
	A. Maximum value 9/10
	B. Minimum value 9/10
	C. Maximum value 11/4
	D. Minimum value 11/4
	E. None of these

Question

Find the range of , if x^2 + 3x -18 < 0

Possible Answers

Selected	Possible Answer
	A. 3
	B. -6 < x < 3
	C. 23
	D. 3>x>2
	E. x>2

Question

A man can feed himself for a certain number of days with $1200. If his cost per day increases by $20, he can feed himself for 30 days less. Find the number of days he used to feed himself earlier.

Possible Answers