Cubic Equation Solver

The Cubic equation is that of the form ax³ + bx² + cx² + d =0. Here a $\neq$ 0.To solve this form of equation there is an excellent tool. 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.

Lets go through some problems on Cubic equations:

Solved Examples

Question 1: Solve the cubic equation: 8x³ - 7x² - 7x + 6 =0
Solution:

Here the given equation 8x³ - 7x² -7x + 6 = 0 is of the form ax³ + bx² + cx + d = 0 where a = 8, b = -7, c = -7, d = 6

Lets use inspection method

put x = 0

8(0)³ - 7(0)² - 7(0) + 6 $\neq$ 0

Hence (x-0) is not a factor

Put x = 1

8(1)³ - 7(1)² - 7(1) + 6
8 - 7 - 7 + 6 = 0

Hence (x-1) is a factor

Lets go for division to get the other factor

8x³ - 7x² -7x + 6 = (x-1)( )

8x²+x-6

x-1)$\overline{8x^3 - 7x^2 -7x + 6}$

8x³ - 8x²

$\overline{ x^2 - 7x + 6}$

x² - x

$\overline{ - 6x + 6}$

- 6x + 6

$\overline{0}$

Hence 8x³ - 7x² -7x + 6 = (x-1)(8x² + x - 6). The roots of equations are x₁ = 1, x₂ = 0.80575, x₃ = -0.9307.

Question 2: Solve the equation: x³ - 3x² - 9x + 27 = 0
Solution:

Here the given equation x³ - 3x² -9x + 27 = 0 is of the form ax³ + bx² + cx + d = 0 where a = 1, b = -3, c = -9, d = 27

Lets use inspection method

put x = 1

(1)³ - 3(1)² - 9(1) + 27 $neq$ 0

Hence (x-1) is not a factor

put x = 2

(2)³ - 3(2)² - 9(2) + 27 $neq$ 0

Hence (x-2) is not a factor

put x = 3
(3)³ - 3(3)² - 9(3) + 27 = 0

Hence (x-3) is a factor

Lets go for division to get the other factor

x³ - 3x² -9x + 27 = (x-3)( )

x² - 9

x-3)$\overline{x^3 - 3x^2 - 9x + 27}$

x³ - 3x²

$\overline{ - 9x + 27}$
-9x + 27

$\overline{ 0}$

Hence x³ - 3x² -9x + 27 = (x-3)(x² - 9). The roots of equations are x₁ = 3, x₂ = -3, x₃ = 3.

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