Question

20 points! Thank you :)

Answer 1

The quadratic expression:

`2 {x}^(2) - 2x - 12`

★ By split middle term,we get

`2 {x}^(2) - 6x + 4x - 12`

`2x(x - 3) + 4( x - 3)`

`(2x + 4) (x - 3)`

`2x + 4 = 0 \: \: and \: \: x - 3 = 0`

`2 x = - 4 \: \: and \: \: x = 3`

`x = - 2 \: \: and \: \: x = 3`

Therefore , the two solution of given quadratic equations is -2 and 3.

Answer 2

`\Large \boxed{x=-2 \ \mathrm{and} \ x=3}`

Explanation:

The quadratic expression is given.

`2x^2-2x-12=0`

Factor the left side of the equation.

`2(x+2)(x-3)=0`

Set the factors equal to 0.

`x+2=0`

`x=-2`

`x-3=0`

`x=3`

The two solutions work in the original equation. The solutions make the equation true.