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:

\(\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}\) , where:

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

Calculations:

Comparing the coefficients:

⇒ \(\dfrac{2}{3} = \dfrac{K}{4} = \dfrac{8}{12}\)

Equate: 2/3 = k/4

⇒ \(\dfrac{K}{4} = \dfrac{2}{3}\)

⇒ K = \(\dfrac{2}{3} \times 4\) = \(\dfrac{8}{3}\)

∴ The correct value of K is \(\dfrac{8}{3}\), which corresponds to option (4).