Question

If $\alpha$ and $\beta$ are the roots of the quadratic equation $4 x^2-4 x+1=0$, then $\alpha^3+\beta^3$ is equal to

(A) $\frac{1}{4}$

(B) $\frac{1}{8}$

(C) 16

(D) 32

Answer 1

$\therefore \quad \alpha+\beta=\frac{4}{4}=1$

$\quad \alpha \beta=\frac{1}{7}$

Now, $\quad \alpha^3+\beta^3=(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta)$

$=1^3-3 \times \frac{1}{4} \times(1)$

$=1-\frac{3}{4}=\frac{1}{4}$

So, The correct option will be (A).