Determining a Quartic Polynomial w/ given zeroes and point

[Math wiz ya rite 09]

Could someone show me how to do this math problem:

Find a quartic (4th degree) polynomial with integer coefficients two of whose zeros are 2/3 and 2 + 3i, and which contains the point (2, -288).

THANKS!

 

[stapel]

You know that factors are solved for zeroes, and thus that zeroes come from factors. So the two zeroes allow you to find two factors. Also, you know (from working with the Quadratic Formula) that complex zeroes come in conjugate pairs, so "2 + 3i" tells you what the third zero, and thus the third factor is.

How far have you gotten with just this information? Please reply showing all of your work and reasoning so far. Thank you.

Eliz.

 

[Math wiz ya rite 09]

thanks for the help!

 

[Math wiz ya rite 09]

stil need an answer

 

[tkhunny]

You don't seem to be getting the idea.

You know that factors are solved for zeroes, and thus that zeroes come from factors. So the two zeroes allow you to find two factors. Also, you know (from working with the Quadratic Formula) that complex zeroes come in conjugate pairs, so "2 + 3i" tells you what the third zero, and thus the third factor is.

How far have you gotten with just this information? Please reply showing all of your work and reasoning so far. Thank you.

TK