A quadratic equation whose one root is 2 cos 2 (π/10) is

Question

A quadratic equation whose one root is 2 cos 2 (π/10) is (A) 4 x2-10 x+5=0 (B) 2 x2-50 x+10=0 (C) 4 x2+10 x+5=0 (D) none of these

Tardigrade Admin · Accepted Answer

Let one root be α ∴ α=2 cos 2 18°=1+ cos 36°=1+((√5+1)/4)=(5+√5/4) . ∴ text other root =β=(5-√5/4) ∴ α+β=(5/2) text and α β=(20/16)=(5/4) ∴ Quadratic equation is 4 x2-10 x+5=0.

Q. A quadratic equation whose one root is $2 cos^{2} \frac{π}{10}$ is

$4 x^{2} - 10 x + 5 = 0$

$2 x^{2} - 50 x + 10 = 0$

$4 x^{2} + 10 x + 5 = 0$

none of these

Let one root be $α$
$∴ α = 2 cos^{2} 1 8^{\circ} = 1 + cos 3 6^{\circ} = 1 + \frac{( 5 + 1 )}{4} = \frac{5 + 5}{4} .$
$∴ other root = β = \frac{5 - 5}{4}$
$∴ α + β = \frac{5}{2} and α β = \frac{20}{16} = \frac{5}{4}$
$∴$ Quadratic equation is $4 x^{2} - 10 x + 5 = 0$ .

Q. A quadratic equation whose one root is 2cos210π​ is

4x2−10x+5=0

2x2−50x+10=0

4x2+10x+5=0