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

Question

State whether the following quadratic equations have two distinct real roots. Justify your answer. (x + 1) (x - 2) + x = 0

Philoid · Accepted Answer

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.