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

Answer 1

The correct option is B

$a^2-2b^2$

Explanation for correct option:

Find the value of ${\mathit{\alpha }}^{\mathbf{2}}\mathbf{+}\mathbf{}{\mathit{\beta }}^{\mathbf{2}}$:

Given that $\alpha$ and $\beta$ are the roots of$x^2-ax+b^2=0$.

$\Rightarrow (\alpha +\beta )=a;\alpha \beta =b^2$

Now, ${\alpha }^2+{\beta }^2$

$$\begin{gathered} \Rightarrow {\alpha }^2+{\beta }^2={(\alpha +\beta )}^2-2\alpha \beta \\ \Rightarrow {\alpha }^2+{\beta }^2=a^2-2b^2 \end{gathered}$$

Hence, the correct option is B.