Question

The value 5 is an upper bound for the zeros of the function shown below. f(x)=x^4+x^3 -11x^2-9x+18

Answer 1

Answer: True

Explanation:
According to the rational zeros theorem, if x=a is a zero of the function f(x), then f(a) = 0.

Given:  f(x) = x⁴ + x³ - 11x² - 9x + 18
From the calculator, obtain
f(5) = 448
f(4) = 126
f(3) = 0
f(2) = -20
f(1) = 0
f(0) = 18
f(-1) = 16
f(-2) = 0
f(-3) = 0

The polynomial is of degree 4, so it has at most 4 real zeros.
From the calculations, we found all 4 zeros as x = -3, -2, 1, and 3.
Therefore
f(x) = (x+3)(x+2)(x-1)(x-3).

For x>3, f(x)increases rapidly. Therefore there are no zeros for x>3.
The statement that x=5 is an upper bound for the zeros of f(x) is true.

Answer 2

Answer:

true

Step-by-step explanation: