Explanation
We are to use Descartes' Rule of Signs to determine the maximum possible number of positive and negative real zeros
for the function:
[tex]2x^4-10x^3+11x^2-15x+12[/tex]
We can observe the number of sign changes in the coefficients as shown below
The sign changes 4 times
So this means that there are 4 sign changes, so there are 4 or 2 or 0 positive real roots
To find the number of negative real roots, substitute x with −x in the given polynomial
The coefficients are
[tex]2,10,11,15,12[/tex]
So there are 0 negative real roots
Thus, the answer is
4 or 2 or 0 positive real roots.
0 negative real roots
The graph below confirms the answer
