Question

How many real roots and how many complex roots exist for the polynomial

Answer 1

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

$F(x)=x^4+x^3-5x^2+x-6$

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

$F(-x)=x^4-x^3-5x^2-x-6$

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.