Question

Solve the following equation by method of factor :-

\[x^4+2x=3x^2\]

Answer 1

First of all \[
x^4-3x^2+2x=0
\]

Answer 2

Second of all \[
x(x^3-3x+2)=0
\]This means \(x=0\) is a solution. Now we just need to find solutions for: \[
x^3-3x+2=0
\]

Answer 3

thanx i gt it :)

Answer 4

You do?

Answer 5

yup :)

Answer 6

What are the remaining solutions?

Answer 7

wait its 3 or 2

Answer 8

x^3 or x^2

Answer 9

@wio

Answer 10

It is \(x^3\) not \(x^2\)

Answer 11

Since \(x^4=x(x^3)\)

Answer 12

oh u plz go on, i thought it is x^2

Answer 13

Cubic equations have no simple solution. However there are guesses which are likely to work.

Answer 14

The leading term is \(1x^3\) and the final term is \(2\).
We take the coefficient of the leading and final term and find their factors.
For the leading term it is just \(1\)
For the final term, it is \(1,2\).

If there is a rational root, it will be of the form \[
\pm \frac{1}{1,2}
\]That is to say, the rational root, if there is one, would be \[
1,-1,1/2,-1/2
\]

Answer 15

So we can try these guesses here.

Answer 16

Putting in \(1\) gives us \((1)^3-3(1)+2=1-3+2=0\)
So fortunately, \(x=1\) is a root.

Answer 17

This means we can factor \(x-1\).

Answer 18

How can u say that the rational roots will be of the form \[\pm \frac{ 1 }{ 1,2 }?\]

Answer 19

It's a particular theorem

Answer 20

can u elaborate it ?

Answer 21

Thing is, it might not even have rational roots.

Answer 22

http://en.wikipedia.org/wiki/Rational_root_theorem

Answer 23

Isn't there any other easier solution ?

Answer 24

For cubic functions?
You can guess and check. There are cubic formulas but they are extremely coplicated.

Answer 25

Calculators will use newton's method to find solutions.

Answer 26

Or bisection method.

Answer 27

Ok thx for ur help & contribution :)