Respuesta :

Answer:

x = - 7, x = 5

Step-by-step 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

kudzordzifrancis

ANSWER

[tex]x = - 7 \: or \: x = 5[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 2x - 35[/tex]

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

[tex] {x}^{2} + 2x - 35 = 0[/tex]

Split the middle term to obtain,

[tex]{x}^{2} + 7x - 5x- 35 = 0[/tex]

Factor by grouping:

[tex]{x}(x + 7) - 5(x + 7)= 0[/tex]

[tex](x + 7)(x - 5) = 0[/tex]

[tex](x + 7) = 0 \: or \: (x - 5) = 0[/tex]

.

[tex]x = - 7 \: or \: x = 5[/tex]

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