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The quadratic equation whose sum of the roots is 11 and sum of squares of the roots is 61 is
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Verified Answer
The correct answer is:
$x^2-11 x+30=0$
Let $\alpha$ and $\beta$ are roots of quadratic equation
$\therefore \alpha+\beta=11$ and $\alpha^2+\beta^2=61$
$\Rightarrow(\alpha+\beta)^2-2 \alpha \beta=61$
$\Rightarrow 121-2 \alpha \beta=61 \Rightarrow \alpha \beta=30$
$\therefore$ Quadratic equation is
$\begin{aligned} & \mathrm{x}^2-(\alpha+\beta) \mathrm{x}+\alpha \beta=0 \\ & \mathrm{x}^2-11 \mathrm{x}+30=0\end{aligned}$
$\therefore \alpha+\beta=11$ and $\alpha^2+\beta^2=61$
$\Rightarrow(\alpha+\beta)^2-2 \alpha \beta=61$
$\Rightarrow 121-2 \alpha \beta=61 \Rightarrow \alpha \beta=30$
$\therefore$ Quadratic equation is
$\begin{aligned} & \mathrm{x}^2-(\alpha+\beta) \mathrm{x}+\alpha \beta=0 \\ & \mathrm{x}^2-11 \mathrm{x}+30=0\end{aligned}$
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