Cubic Equation Solver

Top
**Step 1 :**

**Step 2 :**

**Step 3 :**

The formula ax^{3} + bx^{2} + 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.

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.

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

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

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

Solve the cubic equation: x

^{3}+ x^{2}- 4x + 6 = 0**Step 1 :**Here the given equation x

^{3}+ x^{2}- 4x + 6 = 0 is of the form ax^{3}+ bx^{2}+ 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

x^{3}+ x^{2}- 4x + 6 = (x+3)( )

x2 - 2x + 2

x+3)$\overline{x^3 + x^2 - 4x + 6}$

x^{3}+ 3x^{2}

$\overline{ -2x^2 - 4x + 6}$

-2x^{2}- 6 x

$\overline{2x + 6}$

2x + 6

$\overline{0}$**Answer :**The roots for the function x

^{3}+ x^{2}- 4x + 6 = 0 is x_{1}= -3, x_{2}= 1 + i, x_{3}= 1 - i.Solve the cubic equation: x

^{3}- 13x + 12 = 0**Step 1 :**Here the given equation x

^{3}- 13x + 12 = 0 is of the form ax^{3}+ bx^{2}+ 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

x^{3}- 13x + 12 = (x-1)( )

x^{2}+ x - 12

x-1)$\overline{x^3 - 13x + 12}$

x^{3}- x^{2}

$\overline{ x^2 - 13x + 12}$

x^{2}- x

$\overline{-12x + 12}$

-12x + 12

$\overline{0}$**Answer :**The roots for the function x

^{3}- 13x + 12 = 0 is x_{1}= 1, x_{2}= -4 , x_{3}= 3.