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June 26th, 2012, 12:37 PM   #1
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Polynomial help

I would like to clarify one thing, in questions like,

Find all third degree real polynomials with zeros of -1/2 and 1 -3i
there's always this constant multiplied to the answer, such that the polynomial f(x) = a(answer).

What and why is there a need for a constant to be multiplied? In a general polynomial like 3x^2+x+5, I don't see the need for existence of a constant, unless the constant is 1.

Thank you!
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June 26th, 2012, 12:50 PM   #2
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Re: Polynomial help

Consider that the roots are not changed when multiplying the polynomial by a constant but the polynomial is changed.

For instance:



Yet, the two binomials have the same root.
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June 26th, 2012, 01:07 PM   #3
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Re: Polynomial help

Hello, Tutu!

Quote:
I would like to clarify one thing, in questions like,

Find all third degree real polynomials with zeros of -1/2 and 1 -3i.
There's always this constant multiplied to the answer, such that the polynomial f(x) = a(answer).

What and why is there a need for a constant to be multiplied?
In a general polynomial like 3x^2+x+5, I don't see the need for existence of a constant,
unless the constant is 1.

Thank you!








[color=beige]. . [/color]






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June 26th, 2012, 01:10 PM   #4
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Re: Polynomial help

I see now, thank you thank you thank you!
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