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The roots of $x^{2} + 9 x + k = 0$ are $α a n d α + 1$ , then $k =$

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Detailed Solution

$x^{2} + 9 x + k = 0$

Roots : $α, α + 1$

Sum of roots : $2 α + 1 = - 9$

$2 α = - 10$

$α = - 5$

Product of roots

$α (α + 1) = k$

$- 5 (- 4) = k$

$\Rightarrow k = 20$

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