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.