# Need help with constructing a polynomial

• Nov 14th 2008, 03:24 PM
shipwreck
Need help with constructing a polynomial
The problem is as follows:

Quote:

Construct a polynomial function, reducing all fractions to lowest terms.

Third-degree, with zeros of 1-i, 1+i, and 4, and a leading cofficient of -5.

Any ideas? My book has absolutely no help on this particular type of problem, and I cannot figure it out - I don't even know how to begin...

Thank you in advance for any help...
• Nov 14th 2008, 03:43 PM
mr fantastic
Quote:

Originally Posted by shipwreck
The problem is as follows:

Any ideas? My book has absolutely no help on this particular type of problem, and I cannot figure it out - I don't even know how to begin...

Thank you in advance for any help...

$p(x) = -5(x - 4) (x - [1 - i]) (x - [1 + i]) = -5(x - 4)([x - 1] + i)([x - 1] - i)$

$= -5(x - 4)([x-1]^2 + 1) = -5(x - 4)(x^2 - 2x + 2) = \, ....$