Question

If $\sin \, \theta$ and $\cos \, \theta $ are the roots of the equation $ax^2 - bx + c = 0$, then a, b and c satisfy the relation.

• A. $a^2 + b^2 + 2ac = 0$
• B. $a^2 - b^2 + 2ac = 0$
• C. $a^2 + c^2 + 2ab = 0$
• D. $a^2 - b^2 - 2ac = 0$

Answer 1

Answer: (B)

Given that $\sin \, \theta$ and $\cos \, \theta$ are the roots of the equation $ax^2 - bx + c = 0$, so $\sin \, \theta + \cos \theta = \frac{b}{a} $ and
$\sim \, \theta \, \cos \, \theta = \frac{c}{a}$
Using the identity $(\sin \, \theta + \cos \theta)^2$
$ = \sin^2 \, \theta + \cos^2 \, \theta + 2\sin \, \theta \, \cos \, \theta$, we have
$\frac{b^{2}}{a^{2}} = 1 + \frac{2c}{a}$ or $a^{2} -b^{2} + 2ac =0 $