GRE Quadratic Equations Problems

Question

If $\alpha, \beta$ are the roots of the equation $x ^2 - px + q = 0 \And \alpha ^ 3, \beta ^3$ are the roots of x ^2 -ax + b = 0 then the relation between the coefficients is

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.
	E. None

Question

If the ratio of the roots of ax ^2 + 2bx + c = 0 is same as the ratio of the roots of px ^2 + 2qx + r = 0 then

Possible Answers

Selected	Possible Answer
	A. $\frac{b}{ac} = \frac{q ^2}{pr}$
	B. $\frac{b ^2}{ac} = \frac{q ^2}{pr}$
	C. $\frac{b}{ac} = \frac{q}{pr}$
	D. $\frac{b ^2}{ac} = \frac{p ^2}{qr}$
	E. None

Question

If the quadratic equation $ax ^2 + 2cx + b = 0 \And ax ^2 + 2bx + c = 0 (b \not = c)$ have a common root , then a + 4b + 4c = ?

Possible Answers

Selected	Possible Answer
	A. -2
	B. -1
	C. 1
	D. 0
	E. None

Question

If $\alpha, \beta$ are the roots of x ^2 - x + 1 = 0 then $\alpha ^5 + \beta ^5 =$ ?

Possible Answers

Selected	Possible Answer
	A. 1
	B. 4
	C. 2
	D. 12
	E. None

Question

If the sum of the roots of the equation ax ^2 + bx + c = 0 is equal to sum of their squares, then

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.
	E. None

Question

If the roots of a(b-c)x ^2 + b(c-a)x + c(a-b) = 0 are equal, then a, b, c are in

Possible Answers

Selected	Possible Answer
	A. A.P
	B. H.P
	C. A.G.P
	D. G.P
	E. None

Question

If the roots of the equation ax ^2 + bx + c = 0 are the reciprocals of the roots of the equation px ^2 + qx + r = 0 then

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.
	E. None

Question

If the roots of the equation $\frac{1}{x+p} + \frac{1}{x+q} = \frac{1}{r}$ are equal in magnitude but opposite in sign, then the product of the roots is equal to

Possible Answers

Selected	Possible Answer
	A. $-(\frac{p ^2 + q^2}{2})$
	B. $\frac{p ^2 - q^2}{2}$
	C. $\frac{p ^2 + q^2}{2}$
	D. $-(\frac{p ^2 + q^2-4pq}{2})$
	E. None

Question

If the roots of (b-c)x ^2 + (c-a)x + (a-b) = 0 are equal, then a, b, c are in

Possible Answers

Selected	Possible Answer
	A. H.P
	B. G.P
	C. A.P
	D. A.G.P
	E. None

Question

The value of $\lambda$ in order that the equations $2x ^2 + 5\lambda x + 2 = 0 \And 4x ^2 + 8\lambda x + 3 = 0$ have a common root is given by

Possible Answers

Selected	Possible Answer
	A. -1
	B. 1
	C. 2
	D. $\pm 1$
	E. 0

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GRE Quadratic Equations Problems

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