Question

What polynomial has roots of –6, 1, and 4

Answer 1

if the roots are -6, 1 and 4, that means the monomials obtained after factoring were:

\[(x+6)(x-1)(x-4)\]

So one way to figure out the original polynomial would be to multiply that out. That isnt the only way to do this problem though.

Answer 2

Also by multiplying by any constant you get a good result

Answer 3

Another way would be to take the sum of the roots, the sum of the root products taken two at a time, and the product of the roots.

Sum of roots is: -6 + 1 + 4 = -1

Sum of root products two at a time is : (-6)(1)+(-6)(4)+(1)(4)=-6-24+6=-24

Product of roots is: =(-6)(4)(1)=-24

So the polynomial is x^3+x^2-24x+24

Answer 4

hi joe:D welcome back x)

Answer 5

Hey Lana :) thanks!