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*[x^3-x^2-(3x)/(2)-(5)/(2)]`

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

`\pm 1, \pm 2, \pm (1)/(2), \pm (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]