Question

Is it possible to create a fourth-degree polynomial with only two real zeros?

Answer 1

yes, that's possible. A polynomial with real coefficients if it has complex roots then they will occur as conjugate pair, suppose 2+3i is a root, it has to have 2-3i as a root as well.

Question mentions that 2 roots are real, other two would be a complex conjugate pair. Certainly we can have such a case, but we can't have 1 real root and 3 complex roots for a 4th degree polynomial.
Do you follow?

Answer 2

I think I understand, thank you! But how would I go about making one?

Answer 3

That should be easy, choose any two real values?
tell me two real values

Answer 4

I hate sound stupid, but those are just rational numbers, right?

Answer 5

Real numbers will include rational+ irrational numbers. You can tell any two simple +ve or -ve numbers

Answer 6

Does 12 and 6 work?

Answer 7

yes, for sure

Answer 8

ok, we have out first two zeros, other zeros would be complex.
Ok the polynomial will be of the form
\[(x-12)(x-6)(x-A)(x-B)\]
A and B are complex conjugate roots

Answer 9

Do you know complex no.s ?

Answer 10

I learned about them a while ago, but I don't know. Is it with imaginary i?

Answer 11

yes, you're right.

Answer 12

Okay! So A and B would have imaginary numbers.

Answer 13

yes, and they would be conjugate. of the form
A=c+di
B=c-di