If the values of $k$ for which the equation $x^2+2(k+2) x+$ $6 \mathrm{k}+7=0$ has equal roots are $\mathrm{k}_1$ and $\mathrm{k}_2$, then $\mathrm{k}_1^2+\mathrm{k}_2^2=$

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Aicharya · Accepted Answer

$x^2+2(k+2) x+6 k+7=0$ has equal roots Hence $ \begin{aligned} & b^2-4 a c=0 \ & \left.\Rightarrow[2(k+2)]^2-4(1)(6 \mathrm{k}+7)ight]=0 \ & \Rightarrow k=3,1 \end{aligned} $ Hence $k_1=3, k_2=1$ $ 	herefore \quad k_1^2+k_2^2=10 $

If the values of $k$ for which the equation $x^2+2(k+2) x+$ $6 \mathrm{k}+7=0$ has equal roots are…

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