Chapter 9, Problem 26SGR

To determine

To solve the given equation using graphing.

Answer to Problem 26SGR

The values of x are -3 and 4.

Explanation of Solution

Given information :

The function provided is $x^2-3x-4=0$ .

Formula used :

The given equation would be graphed as a function and the points of x-intercepts would be the results. For these points, the x-coordinate shall serve the purpose of the results.

If the roots are not on points that are integers, use the approximation method to compute the roots.

Else, put the x-intercept value in the equation. If the left-hand and right-hand sides of the equations match, it is a success and those will be the values of x.

Calculation :

The graph of the given equation is

  

The zeroes in the graph are at $\left(-3,0\right)$ and $\left(4,0\right)$ .

Put these values in the given equation to recheck.

  ${\left(-3\right)}^2-\left(-3\right)-12=0$

Putting $x=-3$ in the given equation.

  $=>9+3-12=0$

Simplifying

  $=>12-12=0$

Hence first value of x is a success.

  ${\left(4\right)}^2-\left(4\right)-12=0$

Putting $x=4$ in the given equation.

  $=>16-4-12=0$

Simplifying

  $=>12-12=0$

Hence second value of x is a success.