Roots of Cubic Function
Roots of a cubic function, also known as its zeros or x-intercepts, are the values of x where the function f(x) equals zero.
General form of a cubic function is ax3 + bx2 + cx + d, where a, b, c, and d are constants, and a is not equal to zero.
Factors of Cubic Function
Factors are those expressions which can divide the cubic function exactly without leaving any remainder.
A cubic function has the highest degree ‘3’, hence it only has at most three factors. If m, n and o are the root of the cubic function then the cubic function can be written as:
a(x – m)(x – n)(x – o) = 0
where a is the Leading Coefficient.
Here, (x – m), (x – n), and (x – o) are three factors of cubic function.
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How to Solve Cubic Functions?
To solve any cubic equation follow the steps added below:
Step 1: Start with the cubic function f(x) = ax3 + bx2 + cx + d.
Step 2: Set the function equal to zero: f(x) = 0.
Step 3: Use one of the following methods to find the roots:
Step 4: Factorize if possible.
Step 5: Check for complex roots if necessary.
Step 6: Verify solutions by plugging them back into the original equation.
Express solutions in the desired form (e.g., decimal approximation or exact form).
Cubic Function
A cubic function is a polynomial function of degree 3 and is represented as f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0. Cubic functions have one or three real roots and always have at least one real root. The basic cubic function is f(x) = x3
Let’s learn more about the Cubic function, its domain and range, asymptotes, intercepts, critical and inflection points, and others along with some detailed examples in this article.
Table of Content
- What is Cubic Function?
- Roots of Cubic Function
- Intercepts of a Cubic Function
- Graph of Cubic Function
- Characteristics of Cubic Function
- Inverse of Cubic Function
- Extrema of Cubic Function
- End Behavior of Cube Function
- Graphing Cubic Function
- Cubic Function Vs Quadratic Function
- Examples on Cubic Functions