Question

If sin θ and cos θ are the roots of the equation ax² – bx + c = 0, then a, b and c satisfy the relation ______.

Options

• a² + b² + 2ac = 0

• a² – b² + 2ac = 0

• a² + c² + 2ab = 0

• a² – b² – 2ac = 0

Answer 1

If sin θ and cos θ are the roots of the equation ax² – bx + c = 0, then a, b and c satisfy the relation a² – b² + 2ac = 0.

Explanation:

Given that sin θ and cos θ are the roots of the equation ax² – bx + c = 0

So sin θ + cos θ = `b/a` and sin θ cos θ = `c/a`

Using the identity (sinθ + cos θ)² = sin²θ + cos²θ + 2 sin θ cos θ

We have `b^2/a^2 = 1 + (2c)/a`

or a² – b² + 2ac = 0