Question

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

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

Answer 1

The correct option is A $a^2-b^2+2ac=0$

Sum of the roots $\sin \theta +\cos \theta =\frac{b}{a}$
Product of the roots $\sin \theta .\cos \theta =\frac{c}{a}$
$(\sin \theta +\cos \theta {)}^2=1+2\sin \theta \cos \theta \Rightarrow \frac{b^2}{a^2}=1+\frac{2c}{a}\Rightarrow a^2-b^2+2ac=0.$