Question

Make a conjecture: How many solutions does a quartic equation x 4 + ax 3 + bx 2 + cx + d = 0 have? Explain.

Answer 1

Four

Explanation:

The degree of a polynomial is the highest of the degree of the monomials with non-zero co-efficient. In this problem we are given the polynomial:

`$ x^4 + ax^3 + bx^2 + cx + d = 0 $`

The degree of the polynomial is 4.

For a polynomial of n- degree we have n solutions counting multiplicity.

So for this four degree polynomial we would have 4 solutions. Could be real or complex depending on the equation.