Question

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.

k = 4; f(x) = 2x3 - 2x2 - 3x - 5; Lower bound?

Answer 1

Using synthetic division:     ___________ 2 | 2  3   -4   4          4  14  20     __________     2   7  10  24 Since the results are all positive values this means that 2 is an upper bound.

Answer 2

Answer with explanation:

The given expression is

$f(x)=2x^3-2x^2-3x-5\\\\f(x)=2\times[x^3-x^2-\frac{3x}{2}-\frac{5}{2}]$

By rational root theorem, the possible factors of f(x) is,

  $\pm 1, \pm 2, \pm \frac{1}{2}, \pm \frac{5}{2}$

→So, root of the above equation can't exceed $\frac {5}{2}=2.5$.

So, K=4, can only be upper bound.

→k=4-----[Upper Bound]