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Higher Order Equations

The sum of in...

Question

The sum of integeral roots of the equation $(x^{2} + 3 x)^{2} - (x^{2} + 3 x) - 6 = 0$ is

A

0

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B

3

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C

1

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D

- 3

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Solution

The correct option is D $- 3$
Put $x^{2} + 3 x = y$
$\Rightarrow y^{2} - y - 6 = 0 \Rightarrow y = - 2, 3$
Now
Case $I :$ $x^{2} + 3 x = - 2 \Rightarrow x = - 1, - 2$
Case $I I :$ $x^{2} + 3 x = 3 \Rightarrow x = \frac{1}{2} (- 3 \pm \sqrt{21})$
So the sum of the integral roots of the equation is $- 3$

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Similar questions

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