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Evaluation of a Determinant

If the equati...

Question

If the equations $x^{2} + a x + b = 0$ and $x^{2} + b x + a = 0$ have exactly one common root, then the numerical value of $a + b$ is

A

1

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B

- 1

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C

0

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D

none of these

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Solution

The correct option is A $- 1$
$x^{2} + a x + b = 0 x^{2} + b x + a = 0 l e t c o m m o n r o o t b e t t^{2} + a t + b = 0 - e q 1 t^{2} + b t + a = 0 - e q 2 e q 1 - 2 a t - b t + b - a = 0 (a - b) t = (a - b) t = 1 p u t t i n g t = 1 i n e q 1 t^{2} + a + b = 0 ∴ a + b = - 1$

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