Question

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

• A. $a^2-2b^2$
• B. $2a^2-b^2$
• C. $a^2-b^2$
• D. $a^2+b^2$

Answer 1

Answer: (A)

Since, $\alpha$ and $\beta$ are the roots of $x^2-ax+b^2=0$.
$\alpha +\beta =\frac{-(-a)}{1}=a$
and $\alpha \beta =\frac{b^2}{1}=b^2$
Now, ${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta$
$=a^2-2b^2$