If the sum of the roots of a quadratic equati | vedclass

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(C) Let the roots of the quadratic equation be $\alpha$ and $\beta$. It is given that $\alpha+\beta=1$ and $\alpha^2+\beta^2=13$. We know that $(\alph

Vedclass · Accepted Answer

$x^2-x-6=0$

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(C) Let the roots of the quadratic equation be $\alpha$ and $\beta$. It is given that $\alpha+\beta=1$ and $\alpha^2+\beta^2=13$. We know that $(\alpha+\beta)^2 = \alpha^2+\beta^2+2\alpha\beta$. Substituting the given values: $1^2 = 13 + 2\alpha\beta$. $1 = 13 + 2\alpha\beta$ $\Rightarrow 2\alpha\beta = -12$ $\Rightarrow \alpha\beta = -6$. The quadratic equation is given by $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$. Substituting the values: $x^2 - (1)x + (-6) = 0 \Rightarrow x^2-x-6=0$.

If the sum of the roots of a quadratic equation is $1$ and the sum of the squares of the roots is $13$,then find the equation.

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