Answer:
see explanation
Step-by-step explanation:
Given
5x² - 4 - 8x
To find the zeros equate to zero and rearrange into standard form, that is
5x² - 8x - 4 = 0 ← in standard form
To factor the quadratic
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 = 5 × - 4 = - 20 and sum = - 8
The factors are - 10 and + 2
Use these factors to split the x- term
5x² - 10x + 2x - 4 = 0 ( factor the first/second and third/fourth terms )
5x(x - 2) + 2(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(5x + 2) = 0
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
5x + 2 = 0 ⇒ 5x = - 2 ⇒ x = - [tex]\frac{2}{5}[/tex]
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The sum of the zeros = - [tex]\frac{b}{a}[/tex]
The product of the zeros = [tex]\frac{c}{a}[/tex]
with a = 5, b = - 8 and c = - 4
The sum = 2 - [tex]\frac{2}{5}[/tex] = [tex]\frac{8}{5}[/tex]
and - [tex]\frac{b}{a}[/tex] = - [tex]\frac{-8}{5}[/tex] = [tex]\frac{8}{5}[/tex]
Thus verified
The product = 2 × - [tex]\frac{2}{5}[/tex] = - [tex]\frac{4}{5}[/tex]
and [tex]\frac{c}{a}[/tex] = [tex]\frac{-4}{5}[/tex] = - [tex]\frac{4}{5}[/tex]
Thus verified
