Question

Find the roots of the following quadratic (if they exist) by the method of completing the square.
x²-4√2x+6=0

Answer 1

roots of given quadratic equation is √2 and 3√2

we have to find the roots of quadratic by completing square method.

x² - 4√2x + 6 = 0

⇒x² -4√2x = -6

⇒x² - 2.(2√2).x = -6

adding (2√2)² both sides ,

⇒x² - 2(2√2).x + (2√2)² = -6 + (2√2)²

⇒(x - 2√2)² = -6 + 8 [ here (2√2)² = 8]

⇒(x - 2√2)² = 2

taking square root both sides

⇒(x -2√2) = ±√2

⇒x =2√2 ± √2

⇒x =3√2 , √2

hence roots of given quadratic is 3√2 and √2.