Question

What polynomial has roots of –5, –2, and 4 ?

Answer 1

It's a cubic equation

Answer 2

So the form of the cubic equation is ax^3+bx^2+cx+d=0 Now just plug in the values, form the equations which will give you a,b,c and d

Answer 3

if "a" is a root of a polynomial then (x-a) is a factor of that polynomial...
so here we get the three factors as [x - (-5)] ,[x-(-2)] and [x-4]
i.e (x+5) , (x+2) and (x-4)
so the polynomial is given by their product
(x+5) (x+2) (x-4) ------ (1)
first finding product of (x+5) (x+2) = x² + 5x + 2x + 10 = x² + 7x + 10
so (1) becomes
(x² + 7x + 10) (x-4) = x^3 + 7x^2 + 10x - 4x^2 - 28x - 40
= x^3 + 3x^2 - 18x - 40 is the required polynomial