Question

Find the roots of equation, if they exists, by applying the quadratic formula:

$2x {}^{2} - 2 \sqrt{2} x + 1 = 0$

Answer 1

Given Equation is 2x^2 - 2√2x + 1 = 0.

Here, a = √2, b = -2√2, c = 1.

We know that D = b^2 - 4ac

⇒ (2√2)^2 - 4(2)(1)

⇒ 8 - 8

⇒ 0.

Now,

The equation is:

(i)

⇒ (-b + √D)/2a

⇒ (2√2 + 0)/2(2)

⇒ 2√2/4

⇒ √2/2

(ii)

⇒ (-b - √D)/2a

⇒ (-2√2 - 0)/2(2)

⇒ 2√2/4

⇒ √2/2

Therefore, the roots are √2/2 and √2/2.

Hope it helps!