Solving Cubic Equation Using Graphical Method
A cubic equation is solved graphically when you cannot solve the given equation using other techniques. So, we need an accurate drawing of the given cubic equation. The equation’s roots are the point(s) at which the graph crosses the X-axis if the equation is in the terms of x and if the equation is in the terms of y then the roots of the equation are the points at which the graph cuts the Y-axis.
The number of real solutions to the cubic equation is equal to the number of times the graph of the cubic equation crosses the X-axis.
Example: Find the roots of equation f(x) = x3 − 4x2 − 9x + 36 = 0, using the graphical method.
Solution:
Given expression: f(x) = x3 − 4x2 − 9x + 36 = 0.
Now, simply substitute random values for x in the graph for the given function:
x
-4
-3
-2
-1
0
1
2
3
4
5
f(x)
-56
0
19
40
36
24
10
0
0
16
We can see that the graph has cut the X-axis at 3 points, therefore, there are 3 real solutions.
From the graph, the solutions are: x = -3, x = 3, and x = 4.
Hence, the roots of the given equation are -3, 3, and 4.
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Solving Cubic Equations
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.
Table of Content
- Polynomial Definition
- Degree of Equation
- Cubic Equation Definition
- How to Solve Cubic Equations?
- Solving Cubic Equations
- Solving Cubic Equation Using Factors
- Solving Cubic Equation Using Graphical Method
- Problems Based on Solving Cubic Equations
- Practice Problems on Solving Cubic Equations
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.
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