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 + 4) 2 - 8x = 0

Philoid · Accepted Answer

The equation (x + 4)² - 8x = 0 has no real roots.

Simplifying the above equation,

⇒ x² + 8x + 16 - 8x = 0

∴ x² + 16 = 0

∴ D = b² - 4ac

= (0) - 4(1) (16) < 0

Hence, the roots are imaginary.