Find the value of K if the quadratic equations 2x² + Kx + 8 = 0 and 3x² + 4x + 12 = 0 have both roots common.

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 1)

Answer 1

Given:

The quadratic equations are:

1) 2x² + Kx + 8 = 0

2) 3x² + 4x + 12 = 0

Both equations have the same roots.

Formula used:

If two quadratic equations have the same roots, their corresponding ratios of coefficients must be equal:

, where:

a₁, b₁, c₁ are coefficients of the first equation and a₂, b₂, c₂ are coefficients of the second equation.

Calculations:

Comparing the coefficients:

⇒

Equate: 2/3 = k/4

⇒

⇒ K = =

∴ The correct value of K is , which corresponds to option (4).