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 = 0

Philoid · Accepted Answer

The equation x (1 - x) – 2 = 0 has no real roots.

Simplifying the above equation,

∴ x² – x + 2 = 0

∴ D = b² - 4ac

= (-1)² - 4(1)(2)

= 1 - 8 < 0

Hence, the roots are imaginary.