AP EAMCET · Maths · Quadratic Equation
The quadratic equation whose roots are \(\sin ^2 18^{\circ}\) and \(\cos ^2 36^{\circ}\) is :
- A \(16 x^2-12 x+1=0\)
- B \(16 x^2+12 x+1=0\)
- C \(16 x^2-12 x-1=0\)
- D \(16 x^2+10 x+1=0\)
Answer & Solution
Correct Answer
(A) \(16 x^2-12 x+1=0\)
Step-by-step Solution
Detailed explanation
Since \(\sin ^2 18^{\circ}\) and \(\cos ^2 36^{\circ}\) are the roots of a quadratic equation. \(\therefore \text { Sum of roots }=\sin ^2 18^{\circ}+\cos ^2 36^{\circ}\) \(=\left(\frac{\sqrt{5}-1}{4}\right)^2+\left(\frac{\sqrt{5}+1}{4}\right)^2\)…
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