Question

What are the solutions for x when y is equal to 0 in the following quadratic

function?
y = x² + 10x – 24
OA) X= -4 or x = -6
OB) x = -6 or x = 4
OC) x = -2 or x = 12
OD) x = -12 or x = 2
O E) no real solutions​

Answer 1

D) x = -12 or x = 2

Explanation:

The given quadratic equation is:

`y=x^2+10x-24`

When y=0, we obtain:

`x^2+10x-24=0`

We split the middle term with -2, 12 because their product is is -24 and their sum is 10.

`x^2-2x+12x-24=0`

We factor by grouping to obtain:

`x(x-2)+12(x-2)=0`

`(x-2)(x+12)=0`

Either
`(x-2)=0` or
`(x+12)=0`

Either
`x=2` or
`x=-12`