If one of the root of the equation : ax² + bx + c = 0 is three times the other root, then b² : ac is equal to:

Question

Question

This question was previously asked in

OSSC CGLRE (Mains) Exam (Mathematics) Official Paper (Held On: 23 July, 2023)

Answer 1

Given:

Equation: ax² + bx + c = 0

One root = 3 × Other root

Formula used:

If roots are α and 3α, then:

Sum of roots = α + 3α = -b/a

Product of roots = α × 3α = c/a

Calculation:

4α = -b/a

⇒ α = -b/4a

3α² = c/a

⇒ 3(-b/4a)² = c/a

⇒ 3b²/16a² = c/a

⇒ b² : ac = 16 : 3

∴ The correct answer is 16 : 3.

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