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Location of Roots

If α is one r...

Question

If $α$ is one real root of quadratic equation $x^{2} - 4 x + 1 = 0$ then $2^{n d}$ root $β$ is $(α < β)$

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Solution

The correct option is D

$α = 2 - \sqrt{3} = t a n 15^{\circ}, β = 2 + \sqrt{3} = t a n 75^{\circ}$

$t a n 5 θ = \frac{5 t a n θ - 10 t a n^{3} θ + t a n^{5} θ}{1 - 10 t a n^{2} θ + 5 t a n^{4} θ}$

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