Approximate the greatest real zero of the function g(x)= x^3-3x+1 to the nearest tenth.

Question

I know that there is a zero between -2 and -1, and another between 0 and 1 but do not know how to find it to the nearest tenth. The only example shown in my book uses a calculator and mine does not have instructions for the same functions as the one in the book. I have checked for online calculators and cannot find one to do the calculations either.

Any help would be great as I have to get finished with math this week.

Thanks

Answer 1

Try solving it iteratively: if g(X)=0, then X^3-3X+1=0, so rearrange the equation to read

X = (3X-1)^(1/3)

Not put X = 2, and evaluate the function. You'll get about 1.71. Feed that into the equation again, and you'll get about 1.60. Keep going for a few more iterations until it settles down. Then try feeding it into the original equation and see if it works.