In the quadratic equation ax2 - bx + c = 0, if the given equation has equal roots and the product of both roots is 4, then, what is the ratio of b : c?

In the quadratic equation ax2 - bx + c = 0, if the given equation has equal roots and the product of both roots is 4, then, what is the ratio of b : c? Correct Answer 1 : 1

Given:

ax² + bx + c = 0

Concept Used:

If a quadratic equation (ax² - bx + c = 0) has equal roots, then discriminant should be zero i.e. b² – 4ac = 0

Calculation:

Suppose the roots are α and α.

⇒ α² = 4 = c/a

⇒ α = 2

Or, 4 = c/a      ….(i)

α + α = b/a

⇒ 2α = b/a

⇒ 4 = b/a     …..(ii)

Dividing equation (ii) by equation (i), we have –

⇒ (b/a)/(c/a) = 4/4

⇒ b/c = 1 : 1