Question

Let ​ f(x)=x^2+x−42 ​. Enter the x-intercepts of the quadratic function in the boxes. x = and x =

Answer 1

x = -7, x = 6

Explanation:

f(x) = x² + x − 42

You can use the quadratic formula to find the roots (x-intercepts), or, if it's "factorable", you can use the AC method.

Here, a = 1, b = 1, and c = -42.

The product a times c is -42.

Factors of ac that add up to b are +7 and -6.

So the quadratic factors to:

f(x) = (x + 7) (x − 6)

To find the x-intercepts, we set this equal to 0:

0 = (x + 7) (x − 6)

x + 7 = 0, x − 6 = 0

x = -7, x = 6

Answer 2

We simply have to solve a quadratic equation
`ax^2+bx+c=0` using the quadratic formula

`x_(1,2) = (-b\pm√(b^2-4ac))/(2a)`

In your case,
`a=b=1,\ c=-42`. So, the formula becomes

`x_(1,2) = (-1\pm√(1+168))/(2) = (-1\pm 13)/(2)`

So, if we choose the two signs, we have

`x_1 = (-1-13)/(2)=-7,\quad x_2 = (-1+13)/(2)=6`