Question

Show that the quadratic equation x² – 8x + 18 = 0 has no real solution.

Answer 1

Given: x² – 8x + 18 = 0.

Step-wise calculation:

1. Identify coefficients:

a = 1, b = –8, c = 18

2. Compute the discriminant:

D = b² – 4ac 

= (–8)² – 4 × 1 × 18 

= 64 – 72

= –8

3. Since D < 0, the quadratic has no real roots (a negative discriminant means no real solutions).

The equation x² – 8x + 18 = 0 has no real solution.