Find the root of \( 4m^2 + 6m + 2 = 0 \)

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 1)

Answer 1

Given:

The quadratic equation is 4m² + 6m + 2 = 0

Formula used:

To find the roots of a quadratic equation ax² + bx + c = 0, use the quadratic formula:

m = \(\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)

Where:

a = coefficient of m², b = coefficient of m, c = constant term

Calculation:

Here, a = 4, b = 6, c = 2

⇒ m = \(\dfrac{-6 \pm \sqrt{6^2 - 4 \times 4 \times 2}}{2 \times 4}\)

⇒ m = \(\dfrac{-6 \pm \sqrt{36 - 32}}{8}\)

⇒ m = \(\dfrac{-6 \pm \sqrt{4}}{8}\)

⇒ m = \(\dfrac{-6 \pm 2}{8}\)

Case 1: m = \(\dfrac{-6 + 2}{8} = \dfrac{-4}{8} = -\dfrac{1}{2}\)

Case 2: m = \(\dfrac{-6 - 2}{8} = \dfrac{-8}{8} = -1\)

∴ The roots of the equation are -1/2 and -1. The correct answer is option (3).