If-sin-2-and-cos-2-are-the-roots-of-quadratic-equation-find-the-equation-

Question Number 117101 by harckinwunmy last updated on 09/Oct/20

If \sin^{2} θ and \cos^{2} θ are the roots

of quadratic equation, find the equation .

Answered by bemath last updated on 09/Oct/20

\Rightarrow (x - \sin^{2} θ) (x - \cos^{2} θ) = 0

\Rightarrow x^{2} - (\sin^{2} θ + \cos^{2} θ) x + \sin^{2} θ \cos^{2} θ = 0

\Rightarrow x^{2} - x + \frac{1}{4} \sin^{2} (2 θ) = 0

\Rightarrow {4 x}^{2} - 4 x + \sin^{2} (2 θ) = 0

Commented by harckinwunmy last updated on 09/Oct/20

can you explain how you got \frac{1}{4} \sin^{2} (2 θ) =

from \sin^{2} θ \cos^{2} θ

Commented by bobhans last updated on 09/Oct/20

\Rightarrow \sin^{2} θ \cos^{2} θ = {(\frac{1}{2} . 2 \sin θ \cos θ)}^{2}

\Rightarrow \frac{1}{4} . \sin^{2} (2 θ)

Answered by Olaf last updated on 09/Oct/20

x^{2} - S x + P = 0

\Rightarrow x^{2} - x + \frac{1}{4} \sin^{2} 2 θ = 0

The result is immediate .

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