Question

lf $\sin \theta ,\sin \left(k\theta \right)$ are the roots of $4x^2+2x-1=0$, then $\theta$ is equal to

• A. $-{18}^0$
• B. ${18}^0$
• C. ${36}^0$
• D. $-{36}^0$

Answer 1

The correct option is B ${18}^0$

Consider the equation $4x^2+2x-1=0$
$4x^2+2x-1=0$
$x=\frac{-2\pm \sqrt{4+16}}{8}$
$=\frac{-2\pm \sqrt{20}}{8}$
$=\frac{-1\pm \sqrt{5}}{4}$
Hence, $x=\frac{\sqrt{5}-1}{4}$ and $x=\frac{-\sqrt{5}-1}{4}$

Now, $\frac{\sqrt{5}-1}{4}=\sin {18}^0$ and $\frac{-\sqrt{5}-1}{4}=\sin (-{54}^0)$
Therefore, $x=\sin {18}^0$ and $x=\sin (-{54}^0)$

Therefore, $\theta ={18}^0$ and $k=-3$