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 = 2; f(x) = 5x4 + 4x3 - 2x2 + 2x + 4; Upper bound?

Answer 1

yes correct?

Answer 2

@ZeHanz

Answer 3

If I get your question right, you do need to divide f(x) by (x-2).
This goes as follows:

2 [ 5 4 -2 2 4 ]
10 28 52 108
---------------------+
5 14 26 54 112 <-- remainder

Answer 4

so is it lower or upper level?

Answer 5

**bound

Answer 6

@zordoloom

Answer 7

What do you mean: an upper bound or lower bound for zeros?

Answer 8

i believe so

Answer 9

It seems like it's lower bound. Take a look at this description of bounds:


Upper and Lower Bounds
( http://people.richland.edu/james/lecture/m116/polynomials/zeros.html)
If you have a polynomial with real coefficients and a positive leading coefficient, then ...

Upper Bound
If synthetic division is performed by dividing by x-k, where k>0, and all the signs in the bottom row of the synthetic division are non-negative, then x=k is an upper bound (nothing is larger) for the zeros of the polynomial.
Lower Bound
If synthetic division is performed by dividing by x-k, where k<0, and the signs in the bottom row of the synthetic division alternate (between non-negative and non-positive), then x=k is a lower bound (nothing is smaller) for the zeros of the polynomial.
The zero in the bottom row may be considered positive or negative as needed.

Answer 10

f(2) = 112, there are no real zeros, see attached graph

Answer 11

ohh ok thank u

Answer 12

Thanks, zordoloom, I didn't know that!