SOLUTION: How to find the values of constants a and b if 2+3i is a zero of the polynomial P(x) = ax^3 - 9x^2 + 30x - b?

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Question 1056305: How to find the values of constants a and b if 2+3i is a
zero of the polynomial P(x) = ax^3 - 9x^2 + 30x - b?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
How to find the values of constants a and b if 2+3i is a
zero of the polynomial P(x) = ax^3 - 9x^2 + 30x - b?


Since we are given that 2+3i is a zero, we know that if 
we substitute x = 2+3i in , we 
must get 0.  Substituting:




Since iČ=-1











Then the real and the imaginary parts must both = 0

Setting the imaginary part = 0,

9a-18 = 0
   9a = 18
    a = 2

Setting the real part = 0

  -46a+105-b = 0
-46(2)+105-b = 0
   -92+105-b = 0
        13-b = 0
          13 = b

So



becomes



Edwin
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