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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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Verified Answer
The correct answer is:
10
$x^2+2(k+2) x+6 k+7=0$ has equal roots Hence
$$
\begin{aligned}
& b^2-4 a c=0 \\
& \left.\Rightarrow[2(k+2)]^2-4(1)(6 \mathrm{k}+7)\right]=0 \\
& \Rightarrow k=3,1
\end{aligned}
$$
Hence $k_1=3, k_2=1$
$$
\therefore \quad k_1^2+k_2^2=10
$$
$$
\begin{aligned}
& b^2-4 a c=0 \\
& \left.\Rightarrow[2(k+2)]^2-4(1)(6 \mathrm{k}+7)\right]=0 \\
& \Rightarrow k=3,1
\end{aligned}
$$
Hence $k_1=3, k_2=1$
$$
\therefore \quad k_1^2+k_2^2=10
$$
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