We can solve any equation just by looking at the graph of a function.
Example 1: Solve the following equation x3 + 2x2 - 3x - 6 = 0.
Since we are interested in when this polynomial is zero we can change the question to:
Find the roots (or zeros) of the polynomial funtion
f(x) = x3 + 2x2 - 3x - 6
- Graph the function
-
The roots of this function (3 of them - see zoom) are:
-2, -1.73205080757, and 1.73205080757) (see
Finding Roots of a Function).
These are also the solutions to the original equation.
Example 2: Solve the following equation
= 0
Since we are interested in when this polynomial is zero we can change the question to:
Find the roots of the function
f(x) = .
- Graph the function;
- The roots are found to be -3/2 and 3/2. (see
Finding Roots of a Function).
These are also the solutions to the original equation.
Example 3: Solve the following equation x3 + 2x2 = 3x + 6 .
By subtracting the right hand side from both sides of the inequality we see that this question is the same as Example 1:
Solve the equation x3 + 2x2 - 3x - 6 = 0.
You could even avoid the algebra by entering the left hand side as the function y1 and the right hand side as y2. Unselect these and enter for y3 the difference y1 - y2. This graph will be the same as the one in Example 1.