Question 57642This question is from textbook Applied College Algebra
: Find a polynomial function with real coefficients that has zeros 3 and - 4i, has degree 3 and where P(0) = -96.
This question is from textbook Applied College Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Find a polynomial function with real coefficients that has zeros 3 and - 4i, has degree 3 and where P(0) = -96.
:
We know one factor is (x-3) = 0
:
x = -4i
x^2 = (-4i)^2
x^2 = 16(i^2)
x^2 = 16(-1)
x^2 = -16
x^2 + 16 = 0
:
Factors are: (x-3)(x^2 + 16) = 0
FOIl this:
x^3 - 3x^2 + 16x - 48 = 0
:
However is says P(0) = - 96, the last term in our equation is -48:
Change (x-3) to (2x - 6), we still have a 0 of +3, but if we FOIL this,
:
(2x-6)(x^2 + 16) = 2x^3 - 6x^2 + 32x - 96 = 0
:
This should satisfy the requirement:
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