Solve each inequality in Exercises 86–91 using a graphing utility. x^2 + 3x - 10 > 0

Key Concepts

Inequalities

Inequalities express a relationship where one side is not equal to the other, often using symbols like '>', '<', '≥', or '≤'. In this case, the inequality x^2 + 3x - 10 > 0 indicates that we are looking for values of x that make the quadratic expression positive. Understanding how to manipulate and solve inequalities is crucial for finding the solution set.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax^2 + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. In this problem, the quadratic x^2 + 3x - 10 will be analyzed to determine where it is greater than zero, which involves finding its roots and analyzing the intervals.

Graphing Utility

A graphing utility is a software tool or calculator that allows users to visualize mathematical functions and inequalities. By graphing the quadratic function x^2 + 3x - 10, one can easily identify the regions where the function is above the x-axis, thus solving the inequality. Familiarity with using graphing utilities is essential for efficiently analyzing and interpreting the results of such problems.