Solving Cubic Equations

1. What are Cubic Equations?

Cubic Equations are the algebraic equations in which the maximum power of a variable is 3

2. How do you Factor a Cubic Equation?

We can factor a cubic equation in two ways. First by taking a linear expression common from the given cubic equation, then we will have a linear and a quadratic expression as a product. This quadratic equation can be further factorized to get all the factors. The second method is to find a zero of the given cubic equation by putting random values. The value for which we get the value of the equation to be zero will be one of the zeros of the given cubic equation. Now using the factor theorem form a linear expression let’s say x-a and divide the given cubic equation by this expression which will give a quadratic equation as quotient. This obtained quadratic equation can be further factorized to get all the factors.

3. How do you Solve a Cubic Equation Graphically?

To solve a cubic equation graphically put random values for x in the given cubic equation and solve, you will get the values of y. Plot these obtained values on the graph. Find the coordinates at which the graph is intersecting the x-axis. These coordinates are the solution of the cubic equation.

4. Can all Cubic Equations be Solved Exactly?

Any equation that has odd power must have one real root. Hence, a cubic equation must have at least one real root, unlike a quadratic equation where both roots can be imaginary when the discriminant is less than zero.

5. Can a Cubic Equation have Multiple Solutions?

Yes, cubic equations can have multiple solutions as a cubic equation can have up to three distinct real roots.

6. What do you mean by the Degree of an Equation?

The maximum power possessed by the variable in an equation is called the degree of a polynomial.

7. What is the Difference between a Polynomial and an Equation?

Polynomial is simply an algebraic equation in which the power of the variable is non-negative integer. This polynomial when equated (=) with a numerical value or another polynomial then it is called an Equation.

8. What is the Factor Theorem for cubic equations?

Factor Theorem states that if r is a root (solution) of the cubic equation ax³ + bx² + cx + d = 0, then x – r is a factor of the equation.

9. What if I can’t find exact solutions using formulas?

If finding exact solutions seems impossible, we can use the numerical methods like iterative methods (e.g., Newton’s method) to approximate the roots of the equation.

Learn more about Newton Raphson’s Method.

Cubic Equation is a mathematical equation in which a polynomial of degree 3 is equated to a constant or another polynomial of maximum degree 2. The standard representation of the cubic equation is ax³+bx²+cx+d = 0 where a, b, c, and d are real numbers. Some examples of cubic equation are x³ – 4x² + 15x – 9 = 0, 2x³ – 4x² = 0 etc.

For learning How to Solve Cubic Equations we must first learn about polynomials, the degree of the polynomial, and others. In this article, we will learn about, Polynomials, Polynomial Equations, Solving Cubic Equations Or how to solve cubic equations, and others in detail.