Question

If $\sin \theta$ and $\cos \theta$ are the roots of the equation $a{x}^2-bx+c=0$, 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 $a{x}^2-bx+c=0$, 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 $a^2-b^2+2ac=0$