Question

State whether the quadratic equation (x – √2)² – 2(x + 1) = 0 have two distinct real roots. Justify your answer.

Answer 1

The equation (x – √2)² – √2(x+1)=0 has two distinct and real roots.

Simplifying the above equation,

x² – 2√2x + 2 – √2x – √2 = 0

x² – √2(2+1)x + (2 – √2) = 0

x² – 3√2x + (2 – √2) = 0

D = b² – 4ac

= (– 3√2)² – 4(1)(2 – √2)

= 18 – 8 + 4√2 > 0

Hence, the roots are real and distinct.