GMAT Exam: Quadratic Equations

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

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	A.
	B.
	C.
	D.
	E.

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. $\frac{b}{ac} = \frac{q}{2pr}$
	D. $\frac{b ^2}{ac} = \frac{p ^2}{qr}$
	E. $\frac{b ^3}{2ac} = \frac{p ^3}{2qr}$

Question

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

Possible Answers

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

Question

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

Possible Answers

Selected	Possible Answer
	A. -1
	B. 4
	C. 2
	D. 12
	E. 6

Question

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

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	D.
	E.

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 which of the following is true?

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	A.
	B.
	C.
	D.
	E.

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

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