Question

Without solving, examine the nature of roots of the equation x² – 5x – 2 = 0

Answer 1

Comparing x² – 5x – 2 = 0 with ax² + bx + c = 0;

we get: a = 1, b = – 5 and c = – 2

D = b² – 4ac = (–5)² – 4 × 1 × – 2

= 25 + 8 = 33 ; which is positive but not a perfect square.

∴ The roots of the given equation are irrational and unequal