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Quadratic Equations with Both Roots Common

Given quadrat...

Question

Given quadratic equations $x^{2} + 5 x + p = 0 & 2 x^{2} + q x + 12 = 0$ have both roots common, then $p + q =$

A

16

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B

10

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C

22

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Solution

The correct option is A $16$
Given two quadratic equations:
$x^{2} + 5 x + p = 0 \dots (a)$
$& 2 x^{2} + q x + 12 = 0 \dots (b)$ have two common roots.
Thus, the ratio of corresponding coefficients will be equal
$\Rightarrow \frac{1}{2} = \frac{5}{q} = \frac{p}{12}$
$\Rightarrow q = 10 & p = 6 \Rightarrow p + q = 16$

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