To solve an equation by finding x-intercepts, Cynthia graphed the function y=x^3-5x+|2x-3|. Give several possibilities for the original equation.
See:
http://www.jiskha.com/display.cgi?id=1252206912
To find the x-intercepts of the function y = x^3 - 5x + |2x - 3|, we need to determine the values of x for which y is equal to zero or crosses the x-axis.
First, let's set y = 0 and solve for x.
0 = x^3 - 5x + |2x - 3|
Since there is an absolute value function involved, we need to consider two cases: when 2x - 3 is positive and when it is negative.
Case 1: 2x - 3 > 0
If 2x - 3 > 0, then |2x - 3| = 2x - 3.
0 = x^3 - 5x + 2x - 3
Combining like terms,
0 = x^3 - 3x - 3
We have one possibility for the original equation:
x^3 - 3x - 3 = 0
Case 2: 2x - 3 < 0
If 2x - 3 < 0, then |2x - 3| = -(2x - 3) = -2x + 3.
0 = x^3 - 5x + (-2x + 3)
Combining like terms,
0 = x^3 - 5x - 2x + 3
We have another possibility for the original equation:
x^3 - 7x + 3 = 0
Therefore, two possibilities for the original equation are:
1) x^3 - 3x - 3 = 0
2) x^3 - 7x + 3 = 0