Question

Plz answer my question
Find the roots by quadratic formula.

Answer 1

The 2 roots are
`√(2) \ and \ -3√(2)`.

Explanation:

Given:

`x^2+2√(2)x-6=0`

We need to find the roots of quadratic equation using quadratic formula.

For quadratic expression
`ax^2+bx+c=0`

Quadratic formula
`x= (-b\±√(b^2-4ac))/(2a)`

In Given expression the values of a,b,c are;

`a=1, b=2√(2),c=-6`

We will first find
`√(b^2-4ac)` by substituting the given values;

`√(b^2-4ac)` =
`\sqrt{(2√(2))^2-4*1*(-6) } =√((4*2)+24) =√(8+24)=√(32)= √(16*2)=√((4)^2*2)=4√(2)`

Now Substituting the above value in quadratic formula we get;

`x=(-b\±√(b^2-4ac))/(2a)\\ \\x=(-2√(2) \±4√(2) )/(2*1)\\\\x= (2(-√(2) \±2√(2)))/(2)\\\\x=-√(2) \±2√(2)`

Now we will find 2 different roots as;

`x_1=-√(2) +2√(2)=√(2)\\x_2=-√(2) -2√(2)=-3√(2)`

Hence the 2 roots are
`√(2) \ and \ -3√(2)`.