Question

The roots of equation $4x^2-2\sqrt{5}x+1=0\text{are}$

• A. $\sin {36}^{\circ };\sin {18}^{\circ }$
• B. $\sin {18}^{\circ };\cos {36}^{\circ }$
• C. $\sin {36}^{\circ };\cos {18}^{\circ }$
• D. $\cos {18}^{\circ };\cos {36}^{\circ }$

Answer 1

Answer: (B)

$\sin {18}^{\circ };\cos {36}^{\circ }$

We've, $\sin {18}^o=\frac{\sqrt{5}-1}{4}$ and $\cos {36}^o=\frac{\sqrt{5}+1}{4}$.

Now the given quadratic equation is $4x^2-2\sqrt{5}+1=0$.

The roots of the equation will be $\frac{2\sqrt{5}\pm \sqrt{20-16}}{2\cdot 4}=\frac{\sqrt{5}\pm 1}{4}$.

So the roots are $\sin {18}^o$ and $\cos {36}^o$.