Question

find roots of quadratic equation 2x2-2√2x+1=0 using the quadratic formula

Answer 1

2x² - 2√2x + 1 = 0

2x² - √2x - √2x + 1 = 0

√2x ( √2x - 1 ) - 1 ( √2x - 1 ) = 0

( √2x - 1 ) ( √2x - 1 ) = 0

* ( √2x - 1 ) = 0

x = 1/√2

* ( √2x - 1 ) = 0

x = 1/√2

Answer 2

Given:

• A quadratic equation $2x^2-2\sqrt{2x}+1 = 0$

To Find:

• The roots of the given quadratic equation using the formula.

Solution:

let, $2x^2-2\sqrt{2x}+1 = 0$ → {equation 1}

The general form of a quadratic equation is,

$ax^2+bx+c=0$ → {equation 2}

On comparing equations 1 and 2 we get,

a = 2, b = -2√2, and c = 1

The formula to find the roots of a quadratic equation is given by,

$x=\frac{-b(+/-)\sqrt{ b^2-4ac}}{2a}$

Substitute the values in the above formula. We get,

⇒ x = {-(-2√2)±√[(-2√2×-2√2)-4×2×1]}/(2×2)

In the above step first solve the values present in the brackets.

⇒ x = {2√2±√(8-8)}/4 = (2√2±0)/4

Anything minus zero or plus zero we get the same number. Therefore we get only one root value for the given quadratic equation.

⇒ x = (2√2)/4 = √2/2 = √2/(√2×√2)

In the above step, when we multiply roots twice we get the same number back, ∴ √2×√2 = 2

⇒ x = 1/√2

∴ The root of the given quadratic equation is 1/√2.