Question

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

(x + 4)² – 8x = 0

Answer 1

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.