Question

Solve the following quadratic equations. x2+2√2x−6=0​

Answer 1

Solution:

Given, the quadratic equation is x² + 2√2x - 6 = 0

We have to find the roots of the equation.

By using the quadratic formula,

x = [-b ± √b² - 4ac]/2a

Here, a = 1, b = 2√2 and c = -6

b² - 4ac = (2√2)² - 4(1)(-6)

= 8 + 24

= 32

x = [-2√2 ± √32]/2(1)

x = [-2√2 ± 4√2]/2

x = -√2 ± 2√2

Now, x = - √2 - 2√2 = -3√2

x = -√2 + 2√2 = √2

Therefore, the roots of the equation are √2 and -3√2

Answer 2

Solution:

Given, the quadratic equation is x² + 2√2x - 6 = 0

We have to find the roots of the equation.

By using the quadratic formula,

x = [-b ± √b² - 4ac]/2a

Here, a = 1, b = 2√2 and c = -6

b² - 4ac = (2√2)² - 4(1)(-6)

= 8 + 24

= 32

x = [-2√2 ± √32]/2(1)

x = [-2√2 ± 4√2]/2

x = -√2 ± 2√2

Now, x = - √2 - 2√2 = -3√2

x = -√2 + 2√2 = √2

Therefore, the roots of the equation are √2 and -3√2