## anonymous one year ago 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) = 2x3 + 4x2 + 2x - 4; Lower bound? I believe that it is lower bound, is that correct? How would I solve this?

1. Mertsj

Possible zeros: $\pm\frac{4}{1},\pm\frac{4}{2},\pm\frac{2}{1},\pm\frac{2}{2}, \pm\frac{1}{1},\pm\frac{1}{2}$ or: $\pm4, \pm2, \pm1, \pm\frac{1}{2}$

2. Mertsj

$f(x)=2(x^2+2x^2+x-2)=0$ $x^3+2x^2+x-2=0$

3. Mertsj

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4. Mertsj

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5. Mertsj

So we see there is a zero between 2 and 1/2 and since f(2) is positive and f(1/2) is negative, 2 is an upper bound.