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)

$a^2-2b^2$

Answer 2

The correct answer is A:$a^2-2b^2$
Given that, $\alpha$ and $\beta$ are the roots of $x^{2}-a x+b^{2}=0$.
$\alpha+\beta=\frac{-(-a)}{1}=a$
and $\alpha \beta=\frac{b^{2}}{1}=b^{2}$
$(\alpha+\beta)^2=\alpha^2+\beta^2+2\alpha\beta$
Now, $\alpha^{2}+\beta^{2} =(\alpha+\beta)^{2}-2 \alpha \beta$
\alpha^2+\beta^2$$=a^{2}-2 b^{2}