Question

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x – 1)(x + 2) + 2 = 0

Answer 1

The equation (x – 1)(x + 2) + 2 = 0 has two real and distinct roots.

Simplifying the above equation,

x² – x + 2x – 2 + 2 = 0

x² + x = 0

D = b² – 4ac

= 1² – 4(1)(0)

= 1 – 0 > 0

Hence, the roots are real and distinct.