ACK! I have an calc exam tomorrow and I can't remember my algebra! no, wait.. .I have a calc exam today!! freaking out here. (I need to know the answer to this because I'm practicing modeling behavior of graphs and the original equation is (x^3 -4x -8)/(x+2)... The answer to my original question will give me the x intercepts. Thanks for the help!! oh and if you can, please explain HOW you get your answer. thank you.
2006-11-14 22:31:06 · 5 answers · asked by thesekeys 3 in Science & Mathematics ➔ Mathematics
any way to solve by hand?
2006-11-14 22:54:20 · update #1
it is approximately 2.64943586
I figured it out by trial and error in excel !!!
from question it is evident that X^3-4X =8 so I put following formula in worksheet cell = (A1^3)-(4*A1), and started from 1 in the A1. first approximation revealed that it must be between 2 and 3 and then using successive approximation I kept on trial and got the answer. It may be a little erroneous but what I could do it was all this.
2006-11-14 22:45:36 · answer #1 · answered by chemist 2 · 0⤊ 0⤋
What Chemist has done is rather like what we do in a method called "halving the interval". Having found
f(2) < 0 and f(3) > 0, we look at the value halfway between 2 and 3:
f(2.5) = -2.375 (I think). Since it's neg here and pos at 3, next value we look at is the one halfway between 2.5 and 3.
How do we know there aren't any other zeros? Do you know differential calculus? Using it we can find the two turning points, they are at 2/sqrt3 and -2/sqrt3. f(x) is negative at both these points. Since both "bumps" are below the x axis, it doesn't cross between them, so the root between 2 and 3 is the only one. Chemist certainly deserves the points.
2006-11-15 07:03:24 · answer #2 · answered by Hy 7 · 0⤊ 1⤋
Man there is this way to solve it by hand, its called Cardano's method. I've been trying to figure it out for the last hour! Good luck if you can get it! Check out the site below:
2006-11-15 08:30:05 · answer #3 · answered by thugster17 2 · 0⤊ 0⤋
Use MatLAB brother. The easiest, best and most accurate way.
2006-11-15 06:41:21 · answer #4 · answered by Thilina Guluwita 4 · 0⤊ 0⤋
it will be solved using quardatic eqn....take a=1,b=(-4), and c=-8
put these values in the two below eqn n get the ans...
root 1=-b+(b^2-4*a*c/2a)^(1/2)
root 2=-b-(b^2-4*a*c/2a)^(1/2)
2006-11-15 11:33:35 · answer #5 · answered by virendra s 2 · 0⤊ 2⤋