Question

lf $\sin \theta ,\cos \theta$ are the roots of the equation $a{x}^2+bx+c=0$ then

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

Answer 1

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

$Giventhat\sin \theta and\cos \theta aretherootsoftheequationa{x}^2+bx+c=0⟹\sin \theta +\cos \theta =-\frac{b}{a}and\sin \theta \cos \theta =\frac{c}{a}Now(\sin \theta +\cos \theta {)}^2=si{n}^2\theta +co{s}^2\theta +2\sin \theta \cos \theta \Rightarrow {(-\frac{b}{a})}^2=1+2.\frac{c}{a}\Rightarrow a^2-b^2+2ac=0$