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.
• B.
• C.
• D.

Answer 1

The correct option is B

Since sin $\theta$ and cos $\theta$ are roots of the given quadratic equation, we have sin $\theta$ + cos $\theta =\frac{a}{b}$ and sin $\theta$ and cos $\theta =\frac{c}{a}$ $\Rightarrow (sin\theta +cos\theta {)}^2=\frac{b^2}{a^2}\Rightarrow si{n}^2\theta +co{s}^2\theta +2sin\theta cos\theta =\frac{b^2}{a^2}\Rightarrow 1+2\frac{c}{a}=\frac{b^2}{a^2}\Rightarrow a^2+2ac+b^2=0$