SOLUTION: given that x=3+i is a root of p(x)=3x^4+ax^3+34x^2+bx-20 find the value of a and b if when p(-1)=34. then factor the polynomial completely

Question 1167586: given that x=3+i is a root of p(x)=3x^4+ax^3+34x^2+bx-20 find the value of a and b if when p(-1)=34. then factor the polynomial completely
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The information p(-1)=34 is not needed to solve the problem....

Since x=3+i is a root, x=3-i is another root. The quadratic factor corresponding to those two roots is

Given the leading coefficient and constant term of the polynomial, we know the factorization of the polynomial is of the form

Performing that multiplication yields

We can solve for n knowing that the coefficient of the quadratic term is 34

We can then find the values of a and b, which are the coefficients of the cubic and linear terms of the polynomial:

a = n-18 = -19
b = 10n+12 = 2

ANSWERS: a = -19; b = 2

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