Solve 2x^2 + x – 6 = 0

Explanation:

Given quadratic equation is, 2x² + x – 6 = 0

On solving,

2x² + x – 6 = 0

⇒ 2x² + (4 – 3)x 6 = 0, doing middle term factor

⇒ 2x² + 4x – 3x – 6 = 0

⇒ 2x(x + 2) – 3(x + 2) = 0

→ (x + 2)(2x – 3) = 0

Since if the product of two numbers is zero then at least one is zero.

Either, x + 2 = 0 ⇒ x = -2 x + 2

Or, 2x – 3 = 0 ⇒ 2x = 3 ⇒ x = 3/2

Final Answer:

Hence the solutions of the given quadratic equation 2x² + x – 6 are, x = - 2,3/2.