Question

If $f\left(x\right)=x^2-3x+1$ and $f\left(2\alpha \right)=2f\left(\alpha \right)$ then $\alpha$ is equal to

• A. $\frac{1}{\sqrt{2}}$
• B. $-\frac{1}{\sqrt{2}}$
• C. $\frac{1}{\sqrt{2}}$ or $-\frac{1}{\sqrt{2}}$
• D. none of these

Answer 1

Answer: (C)

$\frac{1}{\sqrt{2}}$ or $-\frac{1}{\sqrt{2}}$

$f\left(x\right)=x^2-3x+1$

$f\left(2\alpha \right)=2f\left(\alpha \right)⟹4{\alpha }^2-6\alpha +1=2{\alpha }^2-6\alpha +2$

${\alpha }^2=\frac{1}{2}⟹\alpha =\pm \frac{1}{\sqrt{2}}$