Solving equation...

zoolanderman2 · 2010-01-26 05:15:17

x³ + 4x² = 0

How to solve this.....? please help, thank you!!

John E. Franklin · 2010-01-26 05:23:25

See how x³ is the same thing as x² times x.
You can use this information to factor the equation:
x²x + 4x² = 0
Take the x² out to the left:
x² ( x + 4 ) = 0
From this you can see that x = -4 will make it all zero, so that's one answer.
And x=0 will make the x² be zero, so that is another answer.

I should like to see a graph of this...

John E. Franklin · 2010-01-26 05:33:11

Oh, about graphing it, you kind of need to have a "y" in place of the zero to graph it.
Like:
y = x³ + 4x²

When y is zero, that is the x-axis, where the curvy graph crosses at -4 or touches at zero, on
the x-axis.

zoolanderman2 · 2010-01-26 05:38:37

Dude i'm so sorry it should be x³ + 4x² = 100 not 0

sorry for wasting your time, but how do i do x³ + 4x² = 100?

zoolanderman2 · 2010-01-26 05:41:45

it says x is between 3 and 4. how do i do this without using trail and improvement

John E. Franklin · 2010-01-26 05:48:00

Okay, I'll cut and paste my above solution and change the numbers.
See how x³ is the same thing as x² times x.
You can use this information to factor the equation:
x²x + 4x² = 100
Take the x² out to the left:
x² ( x + 4 ) = 100
From this you can see that x = ???? will make it 100.
Woops, this is harder!!
How about guess 3 and a half?
3.5 times 3.5 is 12.25 and (3.5 + 4) times that is 12.25 times 7.5, which is 91.875, pretty close!
Go higher...
Guess 3.6
3.6 times 3.6 is 12.96 and (3.6 + 4) times that is 12.96 times 7.6, which is 98.496, getting closer!!

3.62212 is very very close!

Last edited by John E. Franklin (2010-01-26 05:52:15)

zoolanderman2 · 2010-01-26 05:50:20

it's 3.622, but i want to know how to get that without using trial and improvement...

John E. Franklin · 2010-01-26 06:04:52

Click on the picture below
to enlarge. It shows a
formula from wikipedia
that is a last resort, instead
of a cubic method.

zoolanderman2 · 2010-01-26 06:10:03

hi John.....thanks for the formula! my worry now is that i cant even write that in the space that i have to show my working, lol. what was the cubic method you said? i think i am supposed to factorise, or use another method. thanks ^^

(my teacher said none of the ques. are supposed to use the cubic formula)

thanks!

John E. Franklin · 2010-01-26 06:28:55

You've got me stumped now!
Here is something fun to read off the net:

If the formula for the general cubic equation (with no missing terms) is
determined from the (simpler) formula for the cubic equation with no x^2
term, it is seen that the formula for the case of a cubic with no x term is
"a bit simpler" than the formula for the general cubic - but that is still
distinctly more complex than the formula for the cubic with no x^2 term.

bobbym · 2010-01-26 12:44:17

Hi;

I have run off a computer factorization for you;

For past quadratics, roots are usually gotten by iterative methods that use a computer. In other words interval bisection, secant, Newtons, Jenkins-Traub, Bairstow, Graeffe and a hundred eignevalue algorithms. These are all computer methods.

Math Is Fun Forum

#1 2010-01-26 05:15:17

Solving equation...

#2 2010-01-26 05:23:25

Re: Solving equation...

#3 2010-01-26 05:33:11

Re: Solving equation...

#4 2010-01-26 05:38:37

Re: Solving equation...

#5 2010-01-26 05:41:45

Re: Solving equation...

#6 2010-01-26 05:48:00

Re: Solving equation...

#7 2010-01-26 05:50:20

Re: Solving equation...

#8 2010-01-26 06:04:52

Re: Solving equation...

#9 2010-01-26 06:10:03

Re: Solving equation...

#10 2010-01-26 06:28:55

Re: Solving equation...

#11 2010-01-26 12:44:17

Re: Solving equation...

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