Chapter 1, Problem 42REAE

Solution

Solve the inequality $2x^2-11x+5<0$ by graphing it.

The solution of the inequality is $0.5<x<5$ .

Given:

The inequality is $2x^2-11x+5<0$ .

Graph:

Sketch the graph for the parabola $y=2x^2-11x+5$ and use the dotted lines to construct the parabolic graph as the inequality sign is $\left(<\right)$ in the inequality $2x^2-11x+5<0$ .

  

Interpretation:

From the graph it can be interpreted that the graph is an upward dotted parabola with $x-$ intercepts $\left(0.5,0\right)\text{ and }\left(5,0\right)$ . Therefore, the solution for the inequality $2x^2-11x+5<0$ is all points lying inside the shaded region such that $0.5<x<5$ .

Hence the solution for the inequality is $0.5<x<5$ .