What is a quartic function with only the two real zeros give

What is a quartic function with only the two real zeros given?

x = -4 and x = -1

A. y = x⁴ + 5x³ + 5x² + 5x + 4

B. y = x⁴ - 5x³ - 5x² - 5x - 4

C. y = -x⁴ + 5x³ + 5x² + 5x + 4

D. y = x⁴ + 5x³ + 5x² + 5x - 5

Solution

x = -4 and x = -1

quartic equation with given zeros is

y = x^4 + 5x^3 + 5x^2 + 5x + 4

since plugging x = -4 and x = -1 makes the equation equal to zero

(-4)^4 + 5(-4)^3 + 5(-4)^2 + 5(-4) + 4 = 0

(-1)^4 + 5(-1)^3 + 5(-1)^2 + 5(-1) + 4 = 0

hence x =-4 and x = -1 are its zeros