SOLUTION: Suppose that a polynomial function P(x) of degree 3 with rational coefficiants has 2 and -3i as zeroes. what are the following a. find the other zeroes b. write P(x) as a product

Question 858768: Suppose that a polynomial function P(x) of degree 3 with rational coefficiants has 2 and -3i as zeroes. what are the following
a. find the other zeroes
b. write P(x) as a product of its linear factors
c. write P(x) in polynomial form
Found 3 solutions by Fombitz, josgarithmetic, solver91311:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Since is a root then so is
a) 2, 3i, -3i
b)
c)

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Complex roots with imaginary components come as conjugate pairs.
The roots include 3i.

-------Factored form with all linear factors.

-------Factored form with Real coefficients and constant terms.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Complex zeros always come in conjugate pairs, that is, if is a zero of a polynomial then is also a zero of that polynomial.

Since your given zeros are 2 and (which is to say ), the third and final zero must be , or simply

If is a zero of a polynomial, then is a linear factor of the polynomial. Hence the linear factors of the desired polynomial are , or more simply:

You can multiply the factors to derive the standard form polynomial yourself. Hint: do the two complex factors first, remembering that the product of a pair of conjugates is the difference of two squares and that

John

My calculator said it, I believe it, that settles it

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