Question

$\alpha = \sin 36^\circ$ is a root of which of the following equation?

• A. $16x^4 - 10x^2 - 5 = 0$
• B. $16x^4 + 20x^2 - 5 = 0$
• C. $16x^4 - 20x^2 + 5 = 0$
• D. $16x^4 - 10x^2 + 5 = 0$

Answer 1

Answer: (C)

$16x^4 - 20x^2 + 5 = 0$

Answer 2

$\alpha = \sin 36^\circ = x(say)$
$x = \frac{\sqrt{10} - 2\sqrt{5}}{4}$
$⇒$ $16x^2 = 10 - 2\sqrt{5}$
$⇒$ $(8x^2 - 5)^2 = 5$
$⇒$ $16x^4 - 80x^2 + 20 = 0$
$∴$ $4x^4 - 20x^2 + 5 = 0$