Respuesta :
Answer:
5x² - 10x - 15 = 0
Step-by-step explanation:
Given that the roots are x = 3 and x = - 1, then the factors are
(x - 3) and (x + 1) and the quadratic is the product of the factors, that is
f(x) = a(x - 3)(x + 1) ← a is a multiplier
Here a = 5, thus
f(x) = 5(x - 3)(x + 1) ← expand factors using FOIL
= 5(x² - 2x - 3) ← distribute parenthesis by 5
= 5x² - 10x - 15
Thus equation is
5x² - 10x - 15 = 0
The quadratic equation is 5x² - 10x - 15.
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x: ax²+bx+c=0. with a ≠ 0 .
Given:
roots are x = 3 and x = - 1, then
(x - 3) and (x + 1) are the factors
f(x) = a(x - 3)(x + 1)
As, a = 5.
Then,
f(x) = 5(x - 3)(x + 1)
= 5(x² - 2x - 3)
= 5x² - 10x - 15
Learn more about quadratic equation here:
https://brainly.com/question/15262743
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