Answer:
x = - 3, x = [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
Given
f(x) = 4x² + 5x - 21
To obtain the zeros, equate f(x) to zero, that is
4x² + 5x - 21 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 21 = - 84 and sum = + 5
The factors are + 12 and - 7
Use these factors to split the x- term
4x² + 12x - 7x - 21 = 0 ( factor the first/second and third/fourth terms )
4x(x + 3) - 7(x + 3) = 0 ← factor out (x + 3) from each term
(x + 3)(4x - 7) = 0
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
4x - 7 = 0 ⇒ 4x = 7 ⇒ x = [tex]\frac{7}{4}[/tex]
