Question

question 7 of 10
the value -2 is a lower bound for the zeros of the function shown below.
$f(x)=4x^3 - 12x^2 - x + 15$

a. true

b. false

Explanation:

Step1: Apply Rational Root Theorem

Possible rational roots: $\pm1,\pm3,\pm5,\pm15,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{5}{2},\pm\frac{15}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{5}{4},\pm\frac{15}{4}$

Step2: Test x=-1 (between -2 and 0)

$f(-1)=4(-1)^3 -12(-1)^2 -(-1)+15=-4-12+1+15=0$

Step3: Check lower bound

Since $f(-1)=0$, -1 is a zero, which is greater than -2. So -2 is not a lower bound (zeros exist above it).

Answer:

B. False