what is the equation of a polynomial function whose only roots are 1,-2,and 4, has a odd degree, negative leading coefficient,?

x = 1 or x = -2 or x = 4
(x - 1) = 0 or (x + 2) = 0 or (x - 4) = 0
-(x - 1)²(x + 2)²(x - 4) = 0
-x⁵ + 2x⁴ + 11x³ - 8x² - 20x + 16 = 0

Well,

P(x) = - (x - 1)(x + 2)(x - 4)

hope it' ll help !!

Roots of 1, -2, and 4 correspond to factors of (x - 1), (x + 2), and (x - 4). Multiply the factors and the simplest polynomial you'll have is y = x^3 - 3x^2 - 6x + 8. You can't have a negative leading coefficient AND a positive constant term for this; they're always going to share the same sign.