a = sin 36° is a root of which of the following equation?

Option 1 - 16x4 – 10x2 – 5 = 0

Option 2 - 16x4 + 20x2 – 5 = 0

Option 3 - 16x4 – 20x2 + 5 = 0

Option 4 - 16x4 – 10x2 + 5 = 0

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Answered by

Payal Gupta | Contributor-Level 10

8 months ago

Correct Option - 3

Detailed Solution:

$α = s i n 36 ° = x (s a y)$

$∴ x = \frac{\sqrt[]{10 - 2 \sqrt[]{5}}}{4}$

$\Rightarrow 16 x^{2} = 10 - 2 \sqrt[]{5}$

$\Rightarrow 16 x^{4} - 80 x^{2} + 20 = 0$

$∴ 4 x^{4} - 20 x^{2} + 5 = 0$

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