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April 19, 2014

April 19, 2014

Posted by **Akash** on Thursday, April 14, 2011 at 1:03pm.

x^3-3x^2+4=0

Please tell me step wise step as i haven't solved such type of equations before.

Thank You

- Quadratic Equations -
**MathMate**, Thursday, April 14, 2011 at 1:27pmEven you subject is "Quadratic Equations", the problem you submitted is a cubic equation, and there appears to be no typo.

We will solve the cubic as it is posted.

x^3-3x^2+4=0

We note that the coefficients add up to zero if we reverse the sign of x^3, i.e. (-1)-3+4=0

This indicates that x=-1 is a zero.

Use long polynomial division to reduce the equation to:

(x^3-3x^2+4)/(x+1)=x²-4x+4

which is a quadratic equation.

We can solve by factorization:

x²-4x+4 = 0

(x-2)²=0

Therefore x=-1 or x=2(multiplicity=2), i.e. x=-1, x=2 or x=2.

- Quadratic Equations -
**Akash**, Thursday, April 14, 2011 at 2:04pmany other easy method

- Quadratic Equations -
**MathMate**, Thursday, April 14, 2011 at 2:23pmI do not see an easier method except factoring trial and error. For this particular problem, you will probably get the answers by trial factoring quite easily.

Remember that this is a cubic equation, which actually has a solution formula more complicated than the above.

There is also the Newton-Ralphson approximation method by iterations.

The above methods (factoring, long division, quadratic equation) do not introduce any algebraic operation that is beyond secondary school level.

- Quadratic Equations -
**find two consecutive odd integers with a sum of 16. solve n +( n+**, Wednesday, April 10, 2013 at 7:59amN+ ( n+2)=16

- Quadratic Equations -
**find two consecutive odd integers with a sum of 16. solve n +( n+**, Wednesday, April 10, 2013 at 8:01amN+ ( n+2)=16

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