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May 28th, 2010, 11:27 AM   #1
HFH
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Finding Polynomial with Roots of Real and Complex Numbers

Find the polynomial of lowest degree with rational coefficients that has -2 and -3+5i as two of its roots.
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May 28th, 2010, 05:51 PM   #2
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Re: Finding Polynomial with Roots of Real and Complex Numbers

Hello, HFH!

Quote:
Find the polynomial of lowest degree with rational coefficients
that has and as two of its roots.

Complex roots occur in conjugate pairs.
Since is a root, then is also a root.

Hence:[color=beige] .[/color] are factors of the polynomial.


The simplest polynmial is:[color=beige] .[/color]

[color=beige]. . . . . . . . . . . . . . . . . . [/color]

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May 29th, 2010, 07:47 AM   #3
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Equations have roots; polynomials (and other functions) have zeros.
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May 29th, 2010, 01:19 PM   #4
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Re:

Quote:
Originally Posted by skipjack
Equations have roots; polynomials (and other functions) have zeros.
You're quibbling.
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