Question

Is this true?
A quartic function will always have 4 solutions.

Answer 1

Nope. Ofc not. The solutions could have repeats.

Answer 2

Ok, then is it possible for it to have less than 4 solutions without repeats?

Answer 3

It can have an imaginary number solution, not just a real-number solution. If that's what you mean by no-solutions.

Some people say that an imaginary number counts as 'no solution.'

Answer 4

Ah, I see, that's all I wanted to know thanks.
By the way, nooo you passed my smartscore. How is this possible?

Answer 5

The fundamental theorem of algebra states that a complex/real polynomial will always have n solutions if you count the repeated solutions as well, with n being the degree of the polynomial. So for a quartic polynomial, there is always four solutions if you count the repeated roots. Note that for real polynomials you have to count the complex solutions in order for this to work.