SOLUTION: Find a polynomial of degree 4 that has zeros -3, 2, -2 and -1 and with the coefficient of x^2 is -3.

Question 1056898: Find a polynomial of degree 4 that has zeros -3, 2, -2 and -1 and with the coefficient of x^2 is -3.
Found 2 solutions by Boreal, math_helper:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The factors for -3,-2,2, and -1 are
(x+3)(x^2-4)(x+1)=x^4+4x^3-x^2-16x-12
Now multiply everything by 3 which will not change the roots but will make the coefficient of x^2 -3.
3x^4+12x^3-3x^2-48x-36

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
General form of a 4th degree polynomial is:

This can be constructed from the zeros:

The zero at -3 means there is a factor (x+3) (because plugging in x=-3 gives zero)
The zeros at 2,-2, and -1 yield three more factors: (x-2)(x+2) and (x+1), respectively.
Putting all the factors together:
(x+3)(x-2)(x+2)(x+1)
= (x+3)(x+1)(x+2)(x-2) (reordered, will multiply first two, last two next)
=
=
=
The problem said the coefficient of should be -3, since it is already -1, we need to multiply the polynomial by 3:
Ans:
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