Question

State the combination of possible number of positive and negative zeros for each function f(x) = 3x^4 + 20x^2 - 32.

a) Positive zeros: 2, Negative zeros: 1
b) Positive zeros: 2, Negative zeros: 0
c) Positive zeros: 0, Negative zeros: 2
d) Positive zeros: 1, Negative zeros: 2

Answer 1

The function has 2 possible positive zeros and 2 negative zeros.

Step-by-step explanation:

The function is f(x) = 3x^4 + 20x^2 - 32. To find the combination of possible positive and negative zeros, we need to determine the number of sign changes in the function.

Counting the sign changes, we have a positive sign followed by a negative sign, then a positive sign. This means there are 2 possible positive zeros.

Since the function is a fourth-degree polynomial, the total number of zeros, counting multiplicities, will be 4. Therefore, the number of negative zeros will be 4 - 2 = 2.