Question

What are the zeros of the function? F(x) = x^2+2x-35

Answer 1

x = - 7, x = 5

Explanation:

To find the zeros equate f(x) to zero, that is

x² + 2x - 35 = 0

To factorise the quadratic

Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (+ 2)

The factors are + 7 and - 5, since

7 × - 5 = 35 and 7 - 5 = + 2, hence

(x + 7)(x - 5) = 0

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x - 5 = 0 ⇒ x = 5

Answer 2

`x = - 7 \: or \: x = 5`

EXPLANATION

The given function is

`f(x) = {x}^(2) + 2x - 35`

To find the zeros, we equate the function to zero.

`{x}^(2) + 2x - 35 = 0`

Split the middle term to obtain,

`{x}^(2) + 7x - 5x- 35 = 0`

Factor by grouping:

`{x}(x + 7) - 5(x + 7)= 0`

`(x + 7)(x - 5) = 0`

`(x + 7) = 0 \: or \: (x - 5) = 0`

.

`x = - 7 \: or \: x = 5`