Question

Write the quadratic equation whose roots are 3 and -1, and whose leading coefficient is 5.

Answer 1

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