Question

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The zeros of the polynomial 3x^4 - 5x^3 - 62x^2 - 92x - 24 are x = {-2, -1/3, 6}. Determine the intervals where the value of f(x) is a negative value. Check all that apply.

a. -∞ < x < -2
b. -2 < x < -1/3
c. -1/3 < x < 6
d. 6 < x < ∞

Answer 1

• c. -1/3 < x < 6

Explanation:

There are 3 zero's but we see the polynomial is of degree 4.

It means it has 2 same zero's. We can verify it is -2. Since -2 is doubled, it reflects the local minimum and it is on the x-axis.

In reality we need to consider the other two zero's.

It is obvious the negative interval is between -1/3 and 6 since the polynomial is of even degree and has positive leading coefficient.

Correct choice is c.

The graph is attached to confirm the theory.