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March 25, 2017

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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 - ,

    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 - ,

    any other easy method

  • Quadratic Equations - ,

    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 - ,

    N+ ( n+2)=16

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