Question

How many solutions over the complex number system does this polynomial

have?
7x^3 – 33x^4 – 4x² + 3x + 52 = 0
2​

Answer 1

4 solutions counting any possible multiplicity

Explanation:

Recall that if one considers the Complex Number System, a polynomial has as many solutions (including multiplicity) as its degree.

So in this case, where we are considering a polynomial of order 4 Notice that the term
`-\,33\,x^4`, is in reality the leading term (term with the highest power of the variable) of this polynomial.

Therefore, in the Complex Number System, this polynomial would have 4 solutions.