Question

Can a function with the complex roots 5, square root of 2, 3i be a fourth degree polynomial with rational coefficients?

Answer 1

how many roots do this have? 5 roots?

Answer 2

If 3i is a root, then -3i is also a root.
So if the polynomial exists, is could be: \( (x-5)(x-\sqrt{2})(x-3i)(x+3i)\).

Multiply it out so see if the coefficients are rational...

Answer 3

(the √2 seems to be the problem here...)

Answer 4

If all the coefficients are rational it means that it is a yes?

Answer 5

Yes, so you now have to check that...

Answer 6

thanks bro.

Answer 7

YW!