Question

Select two values of x that are roots of this equation x^2+2x-6=0

Answer 1

The roots are

`x_1=-1+√(7)`

`x_2=-1-√(7)`

Explanation:

we know that

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

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

in this problem we have

`x^(2) +2x-6=0`

so

`a=1\\b=2\\c=-6`

substitute in the formula

`x=\frac{-2(+/-)\sqrt{2^(2)-4(1)(-6)}} {2(1)}`

`x=\frac{-2(+/-)√(28)} {2}`

`x=\frac{-2(+/-)2√(7)} {2}`

`x_1=\frac{-2(+)2√(7)} {2}=-1+√(7)`

`x_2=\frac{-2(-)2√(7)} {2}=-1-√(7)`

therefore

The roots are

`x_1=-1+√(7)`

`x_2=-1-√(7)`