Respuesta :
Answer:
see explanation
Step-by-step explanation:
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
Express in standard form, that is 6x² - 7x - 3
product = 6 × - 3 = - 18, sum = - 7
The factors are - 9 and + 2
Use these factors to split the middle term
6x² - 9x + 2x - 3 ( factor the first/second and third/fourth terms )
= 3x(2x - 3) + 1(2x - 3) ← factor out (2x - 3)
= (2x - 3)(3x + 1)
To obtain zeros equate to zero
(2x - 3)(3x + 1) = 0
Equate each factor to zero and solve for x
2x - 3 = 0 ⇒ x = [tex]\frac{3}{2}[/tex]
3x + 1 = 0 ⇒ x = - [tex]\frac{1}{3}[/tex]
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The relationship between the zeros and the coefficients is
sum of zeros = - [tex]\frac{b}{a}[/tex] and
product of zeros = [tex]\frac{c}{a}[/tex]
- [tex]\frac{b}{a}[/tex] = - [tex]\frac{7}{6}[/tex] and
[tex]\frac{3}{2}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{7}{6}[/tex]
[tex]\frac{3}{2}[/tex] × - [tex]\frac{1}{3}[/tex] = - [tex]\frac{1}{2}[/tex] and
[tex]\frac{c}{a}[/tex] = [tex]\frac{-3}{6}[/tex] = - [tex]\frac{1}{2}[/tex]
Verifying both relationships
