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Cubic Equation Tutorial

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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 * math.cos(q³ / 3)
  x₂ = (-Term1 + r₁₃ * math.cos(q³ + (2 * math.PI) / 3)
  x₃ = (-Term1 + r₁₃ * math.cos(q³ + (4 * math.PI) / 3)
   where x₁, x₂ and x₃ are 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 + math.sqrt(discriminant)
     t = r - math.sqrt(discriminant)
     term1 = math.sqrt(3.0) * ((-t + s) / 2)
     r₁₃ = 2 * math.sqrt(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.

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This tutorial will help you dynamically to find the roots of a Cubic Equation.