Question

If sin $\alpha$, cos $\alpha$ are the roots of the equation a$x^2$ + bx + c = 0, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

As given, sin $\alpha$ + cos $\alpha$ = -$\frac{b}{a}$, sin$\alpha$ cos $\alpha$ = $\frac{c}{a}$

To eliminate $\alpha$, we have

1 = ${\sin }^2$ $\alpha$ + ${\cos }^2$$\alpha$ = $(sin\alpha +cos\alpha {)}^2$ - 2 sin $\alpha$ cos $\alpha$

= $\frac{b^2}{a^2}$ - $\frac{2c}{a}$ ⇒ $a^2$ - $b^2$ + 2ac = 0