1.

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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