Question

Use Descartes' Rule of Signs to determine the maximum possible numbers of positive andnegative real zeros for f(x) = 2x4 - 10x³ + 11x2² - 15x+12. Use a graph to verify the numbersof positive and negative real zeros for the function.

Answer 1

Explanation

We are to use Descartes' Rule of Signs to determine the maximum possible number of positive and negative real zeros

for the function:

$2x^4-10x^3+11x^2-15x+12$

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

$2,10,11,15,12$

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