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

The Correct Option is A

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, \(\alpha^{2}+\beta^{2} =(\alpha+\beta)^{2}-2 \alpha \beta\)
\(\alpha^2+\beta^2\)\(=a^{2}-2 b^{2}\)