Question

Find which of the following equations are quadratic:

(x – 4)(3x + 1) = (3x – 1)(x + 2)

Answer 1

(x – 4)(3x + 1) = (3x – 1)(x + 2)

`\implies` 3x² + x – 12x – 4 = 3x² + 6x – x – 2

`\implies` 3x² – 11x – 4 = 3x² + 5x – 2

`\implies` 3x² – 11x – 4 – 3x² – 5x + 2 = 0

`\implies` –16x – 2 = 0

`\implies` 16x + 2 = 0; which is not of the form ax² + bx + c = 0.

∴ Given equation is not a quadratic equation.