Question

Find the roots of the equation 2x² – 2√2 x + 1 = 0 if they exist, by applying the quadratic formula.

Answer 1

2x² – 2√2 x + 1 = 0

Compare given equation with the general form of quadratic equation, which is ax² + bx + c = 0

a = 2, b = – 2√2, c = 1

Find Discriminant:

D = b² – 4ac

= (– 2√2)² – 4 x 2 x 1

= 8 – 8

= 0

Equation has equal root.

Find roots:

x = \(\frac{1}{\sqrt2}\) or x = \(\frac{1}{\sqrt2}\)

Roots of equation are real.