Find the real solutions of the equation by graphing for the equation x2 + 2x + 2 = 0.
An equation in the form of ax2 + bx + c = 0 is a quadratic equation, where a is not equal to 0. It always has a two degree.
Answer: The graphing of the equation shows that there are no real solutions for the equation x2 + 2x + 2 = 0.
Let's find the real solutions.
To graph the above equation x2 + 2x + 2 = 0, put the polynomial expression x2 + 2x + 2 equal to y.
y = x2 + 2x + 2
By substituting the values of x for x coordinates, we get the values for y coordinates.
When x = 0, y = (0)2 + 2(0) + 2 = 2
When x = 1, y = (1)2 + 2(1) + 2 = 5
When x = -2, y = (- 2)2 + 2(- 2) + 2 = 2
When x = 2, y = (2)2 + 2(2) + 2 = 10
The intercepts of the x-axis are the solutions of the equation.
- If the graph touches the x-axis at two points, there are two real solutions for the equation.
- If the graph touches the x-axis at one point, there is only one real solution for the equation.
- If the graph does not touch the x-axis, there are no real solutions.
Following is the graph showing the solutions.
Since the graph has no x-intercepts, therefore the given quadratic equation has no real solution.