Question

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

(x + 1)(x – 2) + x = 0

Answer 1

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

Simplifying the above equation,

x² + x – 2x – 2 + x = 0

x² – 2 = 0

D = b² – 4ac

= (0)² – 4(1)(–2)

= 0 + 8 > 0

Hence, the roots are real and distinct.