

InterviewSolution
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If the roots of the quadratic equation ax2 + bx + c =0 are sinα and cosα, then A) a2 + b2 = c2B) b2 – 2ac = a2C) b2 + 2ac = a2D) a2 2 – 2bc = b2 |
Answer» Correct option is (B) \(b^2-2ac=a^2\) Given quadratic equation is \(ax^2+bx+c=0\) Given that \(sin\;\alpha\) and \(cos\;\alpha\) are roots of the equation \(ax^2+bx+c=0\) \(\therefore\) Sum of roots \(=\frac{-b}a\) \(\Rightarrow\) \(sin\;\alpha+cos\;\alpha\) \(=\frac{-b}a\) ______________(1) & Product of roots \(=\frac ca\) \(\Rightarrow\) \(sin\;\alpha\;cos\;\alpha\) \(=\frac ca\) ______________(2) \(\because\) \(sin^2\alpha+cos^2\alpha=1\) \(\Rightarrow\) \((sin\;\alpha+cos\;\alpha)^2\) \(-2\;sin\;\alpha\;cos\;\alpha=1\) \(\Rightarrow(\frac{-b}a)^2-\frac{2c}a=1\) \(\Rightarrow\) \(\frac{b^2-2ac}{a^2}=1\) \(\Rightarrow\) \(b^2-2ac=a^2\) Correct option is B) b2 – 2ac = a2 |
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