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If the equati...

Question

If the equation $x^{2} + a x + b = 0$ and $x^{2} + b x + a = 0$ have a common root, then the numerical value of a+b is $- 1$ .( Enter 1 if true or 0 otherwise)

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Solution

$α^{2} + a α + b = 0,$
$α^{2} + b α + a = 0$
Subtracting, $α (a - b) - (a - b) = 0 \Rightarrow α - 1 = 0$
Putting $α = 1$ in one of the above equation we have , $1 + a + b = 0$
$∴ a + b = - 1$

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