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

Can anybody tell me step wise step how to solve this quadratic equation?

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 1:27pm
Even 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 2:04pm
any other easy method

- Quadratic Equations -
**MathMate**, Thursday, April 14, 2011 at 2:23pm
I 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 7:59am
N+ ( n+2)=16

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