How to writ a polynomial function of least degree with integral coefficients that has the given of a zero 2i, -2i, 2square root of 2

Question

how to write a polynomial function of least degree with integral coefficients that has the given zeros. 

 

2i, -2i, 2 square root of 2

Answer 1

Hi,

 

I assume you have both positive and negative square root of 2 as zeros, because a radical zero always come in pairs.

 

This is how you construct a polynomial equation that has the given zeros:

 

if your zero is 5, then the polynomial function of least degree is y = x-5 

 

if your zero is -5, then the function is y = x +5.

 

If you have multiple zeros, multiply individual zeros together:

 

Example : zeros are 5 and -5, then the function is y = (x-5)(x+5) so, y = x²  - 25

 

 

Now I guess you already figured out the answer to your own question:  y = (x+2i)(x-2i)(x² -2), y = x⁴ +2x² -8

 

 

If you meant you have both positive and negative 2 times square root of 2 as zeros, then the answer is

 

 y = (x+2i)(x-2i)(x² - 8), that is  y = x⁴ -4x² -32