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Find the equation whose roots are 2 and $-3\frac{1}{2}$ ...

Find the equation whose roots are 2 and $-3\frac{1}{2}$

A.

2x² + 3x + 14 = 0

B.

2x² + 5x + 7 = 0

C.

2x² + 5x - 7 = 0

D.

2x² + 3x - 14 = 0

View answer & explanation

Correct answer is D

x² (sum of roots)x + (product of roots) = 0
Sum of roots $2+-3\frac{1}{2} = -1\frac{1}{2}=-\frac{1}{2}$
Product of roots $=2 \times -3\frac{1}{2}=-7\\ x^2-\left(\frac{-3}{2}\right)x+(-7)=0\Rightarrow 2x^2 + 3x - 14 = 0$

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