Question

how do you solve X^3-4x+3=0

Answer 1

by inspection, 1 is a root

Answer 2

will you be able to solve if you know one of the roots ?

Answer 3

here
its very easy to find,
SUM of co-efficients = 0
hence x=1 must be the root

Answer 4

synthetic division and quadratic formula are your best friends here

Answer 5

agreed,
synthetic or long division
i'd go for synthetic

Answer 6

yes synthetic division
it's the best method to solve this

Answer 7

for ANY polynomial, its easy to determine whether
x=1 or x=-1 is one of the solution

if sum of ALL co-efficients = 0 , then x= 1 is a root

if sum of co-efficients of even exponents of x = sum of co-efficient of odd exponents of x,
then x=-1 is the root

Answer 8

I know how to solve quadratic eq...i just dont get how did u know 1 was a root?? O.o
did u just guess? O.o

Answer 9

no guess
this is acceptable reason
if sum of ALL co-efficients = 0 , then x= 1 is a root

Answer 10

+1 and -1 are the first things to guess and check

Answer 11

if you still don't want to use that

you can use rational root theorem

Answer 12

a cubic has a direct formula but its very messy and very very hard to solve it analytically. so you should always try +1, -1 and every other rational root thats predicted by rational root theorem

Answer 13

woooow...i didnt know that O.o
Thanks a lot Hartnn :D

Answer 14

if you know it,
you will need to check for just these values
+1,-1,+3,-3

Answer 15

also descartes rule of signs makes ur life a bit easy by eliminating few of the roots (doesn't matter for current problem as 3 is a prime)

Answer 16

you're welcome ^_^
you'll get a quadratic after synthetic division

also, you can have a look here
http://openstudy.com/study#/updates/504335bee4b000724d4620b4

Answer 17

for
\(ax^3+bx^2+cx+d =0\)

a,b,c,d are the co-efficients

if a+b+c+d = 0, then x= 1 is the root

example :
x^3 - 4x+6x-3

what are the co-efficients ?

Answer 18

1 -4 and 3 = 0 thankssss :")

Answer 19

1, -4 , 6 , -3
add them,
you get 0

Answer 20

similarly,
let me give you an example for x=-1

x^3 - 3x^2 +3x - 1

what are co -efficients of x^3 and x ?? add them
what are co -efficients of x^2 and constant ?? add them

Answer 21

1-3+3-1 = 0 so whenever it goes equal to 0, it means the root is 1? what about the other thing that x-1 is the factor?

Answer 22

ok, i messed up with the example
for this case too, x=1 is one of the solution, yes
because sum of co-efficients is 0

now if 'a' is a root, (x-a) is a factor!

Answer 23

no prob lol :P i understood the main part :)
it's a factor so i can factorize the main equation?

Answer 24

yes
i mean you can use that for synthetic division
you'll use x=1

Answer 25

and where did those 3 come from? O.o ://