SOLUTION: solve equation 3x^3+19x^2-72x=0 please show steps

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Question 1049044: solve equation
3x^3+19x^2-72x=0
please show steps

Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Rational Roots Theorem will give several roots to check using Synthetic Division. Each root found narrows which roots still need to be found.

72=2%2A36=2%2A6%2A6=2%2A2%2A3%2A6%2A2%2A2%2A3%2A2%2A3=12%2A6
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Try to make a list of all combinations of factors for 72.
system%2872=these%2C2%2A36%2C3%2A24%2C4%2A18%2C6%2A12%2C8%2A9%29
Making a full complete list still takes more work because of division by 3 from the leading term.

Try the PLUSes and MINUSES of 2, 3, 4, 6, 8, 9, 12, 18.
The dividend to use should include all degrees of x less than and equal to 3.... No, not really....
Why?
Because you have x%283x%5E2%2B19x-72%29=0.

You will NOT REALLY NEED Rational Roots Theorem because you have a function of x multiplied by a quadratic in x. JUST FIND THE ZEROS OF highlight_green%283x%5E2%2B19x-72%29; you already know that one of your zeros or roots will be x=0.

Roots from the quadratic factor:
%28-19%2B-+sqrt%2819%5E2%2B4%2A3%2A72%29%29%2F2
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%28-19%2B-+sqrt%281225%29%29%2F2
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%28-19%2B-+35%29%2F2
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-27 and 8


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The three solutions are system%28-27%2C0%2C8%29
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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve equation
3x^3+19x^2-72x=0
~~~~~~~~~~~~~~~~~~~~

3x%5E3%2B19x%5E2-72x = 0  --->

Factor:

x%2A%283x%5E2%2B19x-72%29 = 0.

This equation deploys in two independent equations:


1.  x = 0,   which has the solution x=0,  and


2.  3x%5E2%2B19x-72 = 0.

    Solve this quadratic equation by using the quadratic formula:

    x%5B1%2C2%5D = %28-19+%2B-+sqrt%2819%5E2+%2B4%2A3%2A72%29%29%2F%282%2A3%29 = %28-19+%2B-+35%29%2F6.


    The solutions are x%5B1%5D = 16%2F6 = 8%2F3  and  x%5B2%5D = -54%2F6 = -9.


Answer.  The solutions of the original equation are x=0,  x = 8%2F3  and  x = -9.

Everything written by "josgarithmetic" in his post is wrong from the beginning to the end.
Please ignore it.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
solve equation
3x^3+19x^2-72x=0
please show steps
3x%5E3+%2B+19x%5E2+-+72x+=+0
x%283x%5E2+%2B+19x+-+72%29+=+0
x%283x%5E2+%2B+19x+-+72%29+=+0
x%283x%5E2+%2B+27x+-+8x+-+72%29+=+0

x%283x+-+8%29%28x+%2B+9%29+=+0
Therefore, highlight_green%28matrix%283%2C1%2C+x+=+0%2C+x+=+8%2F3%2C+x+=+-+9%29%29
I do agree with "Ikleyn(7327)" in that the other RESPONDENT'S response should be TOTALLY ignored. I have no idea why this person just keeps
giving incorrect and ridiculously confusing solutions. I've been told that he not only confuses others he tries to help but himself as well.
I wonder when he's going to cease all this confusion and posting of ridiculously incorrect answers.