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Q.
If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to
KCETKCET 2015Complex Numbers and Quadratic Equations
Solution:
Since, $\alpha$ and $\beta$ are the roots of $x^{2}-a x+b^{2}=0$.
$\alpha+\beta=\frac{-(-a)}{1}=a$
and $\alpha \beta=\frac{b^{2}}{1}=b^{2}$
Now, $\alpha^{2}+\beta^{2} =(\alpha+\beta)^{2}-2 \alpha \beta $
$=a^{2}-2 b^{2}$