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Construct a quadratic equation whose roots are \(-\frac{1...

Construct a quadratic equation whose roots are $-\frac{1}{2}$ and 2.

A.

3x²-3x+2=0

B.

3x²+3x-2=0

C.

2x²+3x-2=0

D.

2x²-3x+2=0

E.

2x²-3x-2=0

View answer & explanation

Correct answer is E

If x = $-\frac{1}{2}$ and 2; then

$x + \frac{1}{2} = 0$ and $x - 2 = 0$

$\implies (x + \frac{1}{2})(x - 2) = 0$

$x^2 - 2x + \frac{1}{2}x - 1 = 0$

$x^2 - \frac{3}{2}x - 1 = 0$

$2x^2 - 3x - 2 = 0$

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