If sin α and cos α are the roots of the equation ax 2 + bx + c = 0, then b 2 =

Question

Philoid · Accepted Answer

Equation ax² + bx + c = 0 has and as two roots

sin α + cos α =

sin α × cos α = c/a …eq(1)

…..eq (2)

But sin² α + cos² α = 1

∴ a² (1 + 2 sinα.cos α) = b²

Putting sin α × cos α = c/a, we get,

⇒ b² = a² + 2ac.

If sin α and cos α are the roots of the equation ax2 + bx + c = 0, then b2 =