Question

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

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

Given eqiation is $4x^2-2\sqrt{5}x+1=0$

We know quadratic equation is of the form $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{--2\sqrt{5}\pm \sqrt{4\left(5\right)-4\left(4\right)\left(1\right)}}{4}$

$x=\frac{\sqrt{5}\pm 1}{4}$

Since $sin{18}^0=\frac{\sqrt{5}-1}{4}$ and $\cos {36}^0=\frac{\sqrt{5}+1}{4}$