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If sum of squares of the roots of the equation $x^{2}+k x-b=0$ is $2 b$, what is $k$ equal to?
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Let the roots of the equation $x^{2}+k x-b=0$ be $\alpha$ and $\beta$. Sum : $\alpha+\beta=-k$ and Product : $\alpha \beta=-b$
According to the question, we have
$\quad \alpha^{2}+\beta^{2}=2 b$
$\Rightarrow(\alpha+\beta)^{2}-2 \alpha \beta=2 b$
$\Rightarrow k^{2}+2 b=2 b \Rightarrow k=0$
According to the question, we have
$\quad \alpha^{2}+\beta^{2}=2 b$
$\Rightarrow(\alpha+\beta)^{2}-2 \alpha \beta=2 b$
$\Rightarrow k^{2}+2 b=2 b \Rightarrow k=0$
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