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Chapter 2: Problem 87

Solve each inequality using a graphing utility. $$2 x^{2}+5 x-3 \leq 0$$

Short Answer

Expert verified
It isn't possible to provide the actual numeric intervals without seeing the graph, but the answer will typically be in the format of \((-鈭�, a] \cup [b, 鈭�)\) or \([a, b]\), based on where the graph of the inequality is less than or equal to zero.

Step by step solution

01

Graph the Quadratic Equation

Use a graphing utility to graph the quadratic equation \(2x^2 + 5x - 3 = 0\). Note where the graph crosses or touches the x-axis; these are the roots of the equation.
02

Determine Where the Graph is Less Than or Equal to Zero

The graph will be less than or equal to zero where it is below the x-axis. Identify these sections of the graph.
03

Identify the Solution Intervals

The solution of the inequality \(2x^2 + 5x - 3 \leq 0\) is the intervals of x where the graph is less than or equal to zero. Write these intervals in the correct notation.

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