SOLUTION: "find three polynomial functions of different degrees such that each one has zeros at -2, 1 and 3 (and nowhere else)." I found one polynomial function by doing (x+2)(x-1)(x-3) -

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: "find three polynomial functions of different degrees such that each one has zeros at -2, 1 and 3 (and nowhere else)." I found one polynomial function by doing (x+2)(x-1)(x-3) -      Log On


   

Question 849752: "find three polynomial functions of different degrees such that each one has zeros at -2, 1 and 3 (and nowhere else)."
I found one polynomial function by doing (x+2)(x-1)(x-3) - it came out as x^3-2x^2-5x+6 ; I checked it and it works. But I don't know how to go about finding two other polynomial functions.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You could make one zero have a multiplicity of 2. So for instance, instead of just having the factor "(x+2)", you could have "(x+2)^2"

Expanding out (x+2)^2(x-1)(x-3) will give you a polynomial of degree 4 that has the roots -2, 1 and 3. The root -2 will have a multiplicity of 2. The other two roots will have a multiplicity of 1.

Hopefully this helps you in the right direction. If not, then let me know. Thanks.