Question

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

A. a² – 2ac 

B. a² + 2ac 

C. a² – ac 

D. a² + ac

Answer 1

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

sin α + cos α = \(-\frac{b}{a}\)

sin α × cos α = c/a …eq(1)

\((sin\,a\,+\,cosa)^2=\frac{b^2}{a^2}\)

\(sin^2a\,+cos^2a\,+2\,sina\,cos=\frac{b^2}{a^2}....eq(2)\)

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.