If sin θ and cos θ are the roots of the equation


If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then ab and c satisfy the relation

(a) a2 + b2 + 2ac = 0

(b) a2 – b2 + 2ac = 0

(c) a2 + c2 + 2ab = 0

(d) a2 – b2 – 2ac = 0


Given sinθ and cosθ are roots of ax2 – bx + c = 0

Sum of roots is $\frac{b}{a}$ and product of root is $\frac{c}{a}$

i.e $\cos \theta+\sin \theta=\frac{b}{a}$ and $\cos \theta \sin \theta=\frac{c}{a}$

Since $\sin ^{2} \theta+\cos ^{2} \theta=1$

i. e $(\sin \theta+\cos \theta)^{2}=\sin ^{2} \theta+\cos ^{2} \theta+2 \sin \theta \cos \theta$

i.e $\left(\frac{b}{a}\right)^{2}=1+2 \frac{c}{a}$

i. e $b^{2}=a^{2}+2 a c$

i. e $a^{2}-b^{2}+2 a c$

Hence, the correct answer is option B.

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