SOLUTION: Form a&#8203; fifth-degree polynomial function with real coefficients such that 2i,1-2i, and -5 are zeros and f(0)=200.

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Question 1126935: Form a fifth-degree polynomial function with real coefficients such that 2i,1-2i, and -5 are zeros and f(0)=200.
Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

given:
, if that zero given, the conjugate must also be a zero
, we also have
recall: complex zeros always come in pairs

where is a constant, we put this for the y-intercept condition

Using the fact that , we can solve for .

so, we have

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Complex zeros always appear in conjugate pairs, thus if is a zero, then is also a zero. Hence the 5 zeros of your desired polynomial are: and .

If is a zero of a polynomial function , then is a factor of the polynomial. So, in factored form, your polynomial is:

Multiplying it out is left as an exercise for the student.

John

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

SOLUTION: Form a&#8203; fifth-degree polynomial function with real coefficients such that 2i,1-2i, and -5 are zeros and f(0)=200.

SOLUTION: Form a fifth-degree polynomial function with real coefficients such that 2i,1-2i, and -5 are zeros and f(0)=200.