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Cubic Equation Tutorial

  


Cubic Equation Definition:
        A cubic equation is a polynomial equation of the third degree. The general form is ax3+bx2+cx+d=0, where a ≠ 0.

Cubic Equation Formula :
ax3 + bx2 + cx + d = 0,
where
        a = coefficient of x3
        b = coefficient of x2
        c = coefficient of x and
        d = constant.
Cubic Equation solving formula:
  x1 = (-Term1 + r13 * cos(q3 / 3)
  x2 = (-Term1 + r13 * cos(q3 + (2 * ∏) / 3)
  x3 = (-Term1 + r13 * cos(q3 + (4 * ∏) / 3)
   where  x1 x2and x3are the roots of the cubic equation.

Example 1 :  Calculate the roots(x1, x2, x3) of the cubic equation, x 3 - 4x2 - 9x + 36 = 0

  Step 1:   From the above equation, the value of a = 1, b = - 4, c = - 9 and d = 36.

  Step 2:   To Find X:
           Substitute the values in the formula's below to find the roots. The variable disc is nothing but the discriminant, denoted generally as delta(Δ)
     discriminant(Δ) = q3 + r2
     q = (3c - b2) / 9
     r = -27d + b(9c - 2b2)
     s = r + √ (discriminant)
     t = r - √ (discriminant)
     term1 = √ (3.0) * ((-t + s) / 2)
     r13 = 2 * √ (q)

  Step 3:   We get the roots, x1 = 4, x2 = -3 and x3 = 3. This is an example for real roots in the cubic equation.



Related Calculator:
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