Which of the following is the quadratic equation with roots $7, - 12$ ?

x^{2} - 5 x + 84 = 0

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x^{2} + 5 x - 84 = 0

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x^{2} - 5 x - 84 = 0

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x^{2} + 5 x + 84 = 0

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Solution

The correct option is B $x^{2} + 5 x - 84 = 0$
Given roots are $7, - 12$
Sum of the roots $S = 7 - 12 = - 5$
Product of the roots $P = 7 \times - 12 = - 84$
Hence the required equation is :
$x^{2} - S x + P = 0$
$x^{2} + 5 x - 84 = 0$

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