Question

How many solutions over the complex number system does this polynomial have?. . 2x^4-3x^3-24x^2+13x+12=0

Answer 1

There are going to be four solutions over the complex system since the highest degree of the polynomial is four. The number of solutions will pertain to the highest degree or order of the polynomial.

Answer 2

According to the Fundamental Theorem of Algebra on the Roots of Polynomials, the number of roots is equal to the degree of the polynomial. In this case, the polynomial is a fourth degree polynomial. Therefore, there are 4 solutions to the polynomial which over the complex number system.