Answer:
x = - 7 , x = 5
Explanation:
given the quadratic function
f(x) = x² + 2x - 35
to find the zeros , let f(x) = 0 , 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
use these factors to split the x- term
x² + 7x - 5x - 35 = 0 ( factor the first/second and third/fourth terms )
x(x + 7) - 5(x + 7) = 0 ← factor out (x + 7) from each term
(x + 7)(x - 5) = 0
equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 5 = 0 ⇒ x = 5
the zeros are x = - 7 , x = 5