If alpha and beta are the roots of x^{2}-ax+b | vedclass

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Question

(A) Given the quadratic equation $x^{2}-ax+b^{2}=0$. For a quadratic equation of the form $Ax^{2}+Bx+C=0$,the sum of the roots $\alpha+\beta = -B/A$ a

Vedclass · Accepted Answer

$a^{2}-2b^{2}$

Vedclass · Answer

(A) Given the quadratic equation $x^{2}-ax+b^{2}=0$. For a quadratic equation of the form $Ax^{2}+Bx+C=0$,the sum of the roots $\alpha+\beta = -B/A$ and the product of the roots $\alpha\beta = C/A$. Here,$A=1$,$B=-a$,and $C=b^{2}$. Therefore,$\alpha+\beta = -(-a)/1 = a$ and $\alpha\beta = b^{2}/1 = b^{2}$. We need to find the value of $\alpha^{2}+\beta^{2}$. Using the algebraic identity $\alpha^{2}+\beta^{2} = (\alpha+\beta)^{2}-2\alpha\beta$. Substituting the values,we get $\alpha^{2}+\beta^{2} = (a)^{2}-2(b^{2}) = a^{2}-2b^{2}$.

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b^{2}=0$,then $\alpha^{2}+\beta^{2}$ is equal to

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