GMAT Quadratic Equations Questions

Question

If x, y, z are real and distinct then x ^2 + 4y ^2 + 9z ^2 -6yz - 3zx - 2xy is always

Possible Answers

Selected	Possible Answer
	A. Zero
	B. Nonnegative
	C. Negative
	D. Positive
	E. None of these

Question

The condition that one root of the equation ax^2+bx+c=0 exceeds the other by is

Possible Answers

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

Question

If $\alpha, \beta$ are the roots of 3x ^2 + 5x - 7 = 0

then the value of $(\frac{1}{3\alpha + 5}) ^ 2 + (\frac{1}{3\beta + 5}) ^ 2$ is

Possible Answers

Selected	Possible Answer
	A. $\frac {67}{63}$
	B. $\frac {109}{63}$
	C. $\frac {109}{441}$
	D. $\frac {67}{441}$
	E. None of these

Question

If the two equations x^2-cx+d=0 and x^2-ax+b=0 have a common root and the second equation has equal roots, then

Possible Answers

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

Question

If $\alpha \not = \beta$ but $\alpha^2=2\alpha - 3; \beta ^2 = 2\beta - 3$ then the equations whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is

Possible Answers

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

Question

If the roots of the equation 12x ^2 + mx + 5 = 0 are in the ratio 5 : 4, then ?

Possible Answers

Selected	Possible Answer
	A. $6\sqrt{3}$
	B. $\pm 6\sqrt{3}$
	C. $9\sqrt{3}$
	D. $\pm 9\sqrt{3}$
	E. None of these

Question

If the difference of the roots of the equation x ^2 - bx + c = 0 is equal to the difference of the roots of the equation x^2 -cx+b=0 and $b \not = c$ then find $\frac{b ^ 2 - c ^ 2]{b - c}$ .

Possible Answers

Selected	Possible Answer
	A. 0
	B. -4
	C. 2
	D. 4
	E. None of these

Question

If $\alpha, \beta$ are the roots of ax^2+bx+c=0

then the value of $(\frac{\beta}{a\alpha + b}) ^ 4 - (\frac{\alpha}{a\beta + b}) ^ 4$ is

Possible Answers

Selected	Possible Answer
	A. $\frac{1-a}{a ^4}$
	B. $\frac{1+a}{a ^3}$
	C.
	D.
	E. None of these

Question

If the roots of px^2+2qx+r = 0 and $qx ^2 - 2\sqrt{pr}x + q = 0$ are simultaneously real, then

Possible Answers

Selected	Possible Answer
	A.
	B. $2q = \sqrt{pr}$
	C. $p = q; r \not = 0$
	D.
	E. None of these

Question

If the coefficient of in the quadratic equation x^2 +px+q=0 was taken as 17 in place of 13,its roots were found to be -2 and -15 the roots of the original equation are

Possible Answers

Selected	Possible Answer
	A. -4,-9
	B. -3,-10
	C. 4,9
	D. 3,10
	E. None of these

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GMAT Quadratic Equations Questions

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