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) + 2 = 0

Philoid · Accepted Answer

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.