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Which of the following quadratic equations has \(-\frac{1}{2...

Which of the following quadratic equations has $-\frac{1}{2}$ and $\frac{3}{4}$ as its roots?

A.

8x² + 11x - 3 = 0

B.

8x² -11x – 3 = 0

C.

8x² + 2x -3 = 0

D.

8x² - 2x – 3 = 0

View answer & explanation

Correct answer is D

X² - (sum of the roots)x + (product of the roots) = 0
Sum of the roots $= -\frac{1}{2}+\frac{3}{4} = \frac{-2+3}{2}=\frac{1}{4}$
Product of the roots = $-\frac{1}{2}\times \frac{3}{4}=\frac{-3}{8}\\ X^2-\left(\frac{1}{4}\right)x-\frac{3}{8} = 0. Taking \hspace{1mm}the\hspace{1mm} common$
$8x^2-2x-3=0$ ;

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