Question

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$2x^2-2x-3=0$

Short answer

The solutions to the equation $2x^2-2x-3=0$ lie between -1 and 0, 1 and 2.

Step-by-step solution

Step 1. Given Information.

Given to solve the equation $2x^2-2x-3=0$ by graphing. And if the exact roots cannot be found, the consecutive integers between which the roots are located are to be determined.

Step 2. Explanation.

A quadratic equation has a real solution where the graph of the related function crosses or touches the x-axis.

Graphing the given equation using graphing calculator:

From the given graph, the function crosses the x axis between -1 and 0 and then in between 1 and 2.

Hence the solutions to the equation $2x^2-2x-3=0$ lie between -1 and 0, 1 and 2.

Step 3. Conclusion.

Therefore, the solutions to the equation $2x^2-2x-3=0$ lie between -1 and 0, 1 and 2.