If \(\sin (\alpha)\) and \(\cos (\alpha)\) are the roots of the equation \(a x^{2}+b x+c=0\), then \(b^{2}\) is
Question and options
If and are the roots of the equation , then is
Answer and explanation
Correct answer: C - \(a^{2}+2 a c\)
sin + cos = -b/a and sin x cos = c/a. Squaring: 1 + 2c/a = b^2/a^2, so b^2 = a^2 + 2ac.
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