How do you find all solutions real and complex on the following problem?
f(x)= (x^5)-(5x^4)+(12x^3)-(24x^2)+(32x)-16
thanks.
2007-10-21 17:57:33 · 4 answers · asked by Coma White 5 in Science & Mathematics ➔ Mathematics
By trial and error method.
try all factors of 16
such as -1,1,-2,2,-4,4,8,-8,...
using excel calculations will be quicker.
2007-10-21 18:02:45 · answer #1 · answered by iyiogrenci 6 · 0⤊ 0⤋
These are always nasty. Take all of the factors of the last term (16), and put them over all of the factors of the leading coefficient. In this case, since the leading coefficient is 1, you're going to have all whole numbers (thank goodness), so your possible real roots are (+/-)1, (+/-)2, (+/-)4, (+/-)8, (+/-)16. All of your real roots are going to be on this list. Just test them out one by one using synthetic division until you can (hopefully) factor the thing to a quadratic. For example, start out with positive 1. Divide the whole mess by (x-1), then divide the quotient (assuming there is no remainder) by the next root you find, until the largest exponent you're left with is 2. At that point, you can use the Quadratic formula to find the complex solutions.
I hope this has helped you out some.
2007-10-21 18:11:42 · answer #2 · answered by Naomi 3 · 0⤊ 0⤋
im sorry i had forgooten it.
congratulation for u, for your question which so wonderful.
hi hi hi
2007-10-21 18:09:04 · answer #3 · answered by Anonymous · 0⤊ 0⤋
that is easy, all you have to do is OW OH MY GOD I GOT SHOT IN THE ARM OPIJKHBZ
2007-10-21 18:02:46 · answer #4 · answered by Anonymous · 0⤊ 0⤋