Find the roots of the following quadratic (if they exist) by the method of completing the square. x^2 - 4√2x + 6 = 0

Question

Find the roots of the following quadratic (if they exist) by the method of completing the square.

\(x^2-4\sqrt{2x}+6=0\)

Answer 1

Given: \(x^2-4\sqrt{2x}+6=0\)

To find: the roots of the following quadratic (if they exist) by the method of completing the square.

Solution:

We have to make the quadratic equation a perfect square if possible or sum of perfect square with a constant.

Step 1: Make the coefficient of x² unity.In the equation ,The coefficient of x² is 1.

Step 2: Shift the constant term on RHS,

\(\Rightarrow x^2-4\sqrt{2x}=-6\)

Step 3: Add square of half of coefficient of x on both the sides.

Step 4: Apply the formula, (a - b)² = a² - 2ab + b² on LHS and solve RHS,Here a=x and \(b=2\sqrt{2}\)

As RHS is positive, the roots exist.Now,take square root on both sides,