SOLUTION: Hi! Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions. S has degree 4, and zeros 3i and 4i thanks for your h

Question 199851: Hi!
Find a polynomial with integer coefficients and a leading coefficient of one that satisfies the given conditions.
S has degree 4, and zeros 3i and 4i
thanks for your help!
Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Remember that if you have a complex root, you also have the congugate root.
.
y= (x+3i)(x-3i) (x+4i)(x-4i)
.
y = (x^2 -9i^2) (x^2 -16i^2),,,,with i^2 =(-1)
.
y = (x^2 +9) ( x^2 +16)
.
y= x^4 +25x^2 + 144
.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

See the answer to Question 199809.

http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Polynomials-and-rational-expressions.faq.question.199809.html

Here you are looking for a polynomial of degree 4, and you are given that two of the four zeros are and , which, expressed in complex number form are and . But recall that complex roots always occur in conjugate pairs, therefore the other two zeros are and . Hence the four factors of the desired polynomial are:

Hint: Each of the two pairs of conjugates will result in a difference of two squares binomial, and remember that

John

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