Solve cubic equations of the form ax³ + bx² + cx + d = 0, set decimal precision, and plot the graph.
ax³ + bx² + cx + d = 0
This calculator solves cubic equations of the form ax³ + bx² + cx + d = 0 using Cardano’s Method. It calculates all real and complex roots with adjustable precision and plots the cubic graph instantly for better visualization.
Enter the four coefficients:
The calculator automatically computes all three roots of the cubic equation.
You can control the number of decimal places:
This ensures accuracy based on your required level of detail.
The calculator plots the cubic function:
This helps you understand how the roots relate to the curve.
The calculator updates instantly:
1️⃣ Enter coefficients a, b, c, and d.
2️⃣ The calculator first converts the equation into a depressed cubic form using substitution:
x = t − (b / 3a)
3️⃣ It computes values:
p = B − (A² / 3)
q = (2A³ / 27) − (AB / 3) + C
4️⃣ The discriminant determines the nature of roots:
• If D > 0 → One real root & two complex roots
• If D = 0 → Multiple real roots
• If D < 0 → Three distinct real roots
5️⃣ Roots are calculated using Cardano’s formula and rounded to your selected precision.
6️⃣ The cubic function is plotted over the selected x-range.
This method guarantees all possible roots (real and complex) of the cubic equation.
Consider the equation:
x³ - 6x² + 11x - 6 = 0
The calculator computes:
Roots: 1, 2, 3
The graph shows the curve intersecting the x-axis at x = 1, 2, and 3, confirming the three real solutions.
Everything you need to know about solving cubic equations and plotting their graphs online.
This calculator solves cubic equations of the form ax³ + bx² + cx + d = 0 using Cardano’s method. It computes all three roots (real or complex) and also plots the corresponding cubic graph.
You must enter numerical values for coefficients a (x³), b (x²), c (x), and d (constant). The calculator automatically computes the roots once valid values are provided.
If a = 0, the equation is no longer cubic. The calculator will display an error message because Cardano’s method only applies to true cubic equations.
Yes. If the discriminant is positive, the calculator returns one real root and two complex conjugate roots in the form a ± bi. All roots are displayed clearly.
When the discriminant is negative, the equation has three distinct real roots. The calculator computes all three using trigonometric formulas derived from Cardano’s method.
The decimal precision field allows you to choose how many decimal places the roots are rounded to. You can set precision between 0 and 10 decimal places.
The calculator plots the function y = ax³ + bx² + cx + d using a dynamic line chart. The graph updates automatically when you change coefficients or adjust the x-range.
Yes. You can enter custom initial and final x-values for plotting. If left empty, the default range is from -10 to 10.
Yes. If the discriminant equals zero, the calculator identifies repeated roots and clearly labels the repeated value.
Yes. Use the “Clear all” button to reset inputs and hide results, or use the “Reload calculator” button to fully restore the default state.
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