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Q.

If $\sin θ and \cos θ$ are the roots of the equation $a x^{2} + b x + c = 0$ then a, b and c satisfy the relation

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a

$a^{2} + b^{2} + 2 a c = 0$

b

$a^{2} - b^{2} + 2 a c = 0$

c

$a^{2} + c^{2} + 2 a b = 0$

d

$a^{2} - b^{2} - 2 a c = 0$

answer is B.

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Detailed Solution

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$\sin θ \cos θ = c / a$

$\begin{array}{l} \Rightarrow (\sin θ + \cos θ)^{2} = b^{2} / a^{2} \\ \Rightarrow \sin^{2} θ + \cos^{2} θ + 2 \sin θ \cos θ = b^{2} / a^{2} \\ \Rightarrow 1 + 2 \frac{c}{a} = \frac{b^{2}}{a^{2}} \Rightarrow a^{2} + 2 a c - b^{2} = 0 \end{array}$

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