Find the real solutions of the equation by graphing. x2 + 2x + 2 = 0
Solution:
Given, x2 + 2x + 2 = 0
We have to find the real solutions of the equation by graphing.
By substituting the value of x for x coordinates, we get the values of y coordinates.
1) When x = 0
⇒ y = x2 + 2x + 2
⇒ y = (0)2 + 2(0) + 2
⇒ y = 2
2) when x = 1
⇒ y = x2 + 2x + 2
⇒ y = (1)2 + 2(1) + 2
⇒ y = 1 + 2 + 2
⇒ y = 5
3) When x = 2
⇒ y = x2 + 2x + 2
⇒ y = (2)2 + 2(2) + 2
⇒ y = 4 + 4 + 2
⇒ y = 10
4) When x = -2
⇒ y = x2 + 2x + 2
⇒ y = (-2)2 + 2(-2) + 2
⇒ y = 4 - 4 + 2
⇒ y = 2
The intercepts of the x-axis are the solutions of the equation.
a) If the graph touches the x-axis at two points, there are two real solutions for the equation.
b) If the graph touches the x-axis at one point, there is only one real solution for the equation.
c) If the graph does not touch the x-axis, there are no real solutions.
Since the graph has no x-intercepts, there is no real solution.
Therefore, the given quadratic equation has no real solution.
Find the real solutions of the equation by graphing. x2 + 2x + 2 = 0
Summary:
By graphing, the quadratic equation x2 + 2x + 2 = 0 has no real solution.