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Cubic Equation Solver
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The formula ax3 + bx2 + cx + d = 0 is said to be the cubic equation if a $\neq$ 0. If d = 0 then the given equation becomes quadratic when all its terms is divided by x. The cubic equations can have real as well as imaginary roots.
Cubic equation Calculator is a online tool to solve the cubic equation. You just have to enter the cubic equation in the block provided and get its roots instantly.
Default cubic equation is given in the calculator below. On clicking "Solve", you will find the roots of the equation by using inspection method and by dividing the factors.
 

Steps for Cubic Equation Solver

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Step 1 :  

Read the problem and take down the given function f(x).



Step 2 :  

Use inspection method and put x by different values till you get f(x) =0. Take that number as the factor value.



Step 3 :  

Now divide that factor with the function given to get its other factors.



Problems on Cubic Equation Solver

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  1. Solve the cubic equation: x3 + x2 - 4x + 6 = 0


    Step 1 :  

    Here the given equation x3 + x2 - 4x + 6 = 0 is of the form ax3 + bx2 + cx + d = 0 where a = 1, b = 1, c = -4, d = 6



    Step 2 :  

    Lets use inspection method
    put x = -1
    f(-1) = (-1)3 + (-1)2 - 4(-1) + 6 $\neq$ 0
    (x+1) is not a factor
    Put x = -2
    f(-2) = (-2)3 + (-2)2 - 4(-2) + 6 $\neq$ 0
    (x+2) is not a factor
    Put x = -3
    f(-3) = (-3)3 + (-3)2 - 4(-3) + 6
          = -27 + 9 + 12 + 6
          = 0
    Hence (x+3) is a factor




    Step 3 :  

    Lets go for division to get the other factor
    x3 + x2 - 4x + 6 = (x+3)(  )
            x2 - 2x + 2
    x+3)$\overline{x^3 + x^2 - 4x + 6}$
           x3 + 3x2
        $\overline{ -2x^2 - 4x + 6}$
           -2x2 - 6 x
        $\overline{2x + 6}$
            2x + 6
                $\overline{0}$



    Answer  :  

    The roots for the function x3 + x2 - 4x + 6 = 0 is x1 = -3, x2 = 1 + i, x3 = 1 - i.



  2. Solve the cubic equation: x3 - 13x + 12 = 0


    Step 1 :  

    Here the given equation x3 - 13x + 12 = 0 is of the form ax3 + bx2 + cx + d = 0 where a = 1, b = 0, c = -13, d = 12



    Step 2 :  

    Lets use inspection method
    put x = 1
    f(1) = (1)3 - 13(1) + 12


           = 0
    (x-1) is a factor



    Step 3 :  

    Lets go for division to get the other factor
    x3 - 13x + 12 = (x-1)(  )
            x2 + x - 12
    x-1)$\overline{x^3 - 13x + 12}$
           x3 - x2
        $\overline{ x^2 - 13x + 12}$
            x2 -  x
        $\overline{-12x + 12}$
            -12x + 12
                $\overline{0}$



    Answer  :  

    The roots for the function x3 - 13x + 12 = 0 is x1 = 1, x2 = -4 , x3 = 3.



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