Chapter 9, Problem 19MCQ

To determine

To solve equation by graphing

Answer to Problem 19MCQ

  $x=0.4,2.6$

Explanation of Solution

Given information :

The function provided is $-x^2+3x-1=0$

Graph :

  

Interpretation :

To solve the equation using graphing method, the equation is rewritten in standard form and the related function $f(x)=a{x}^2+bx+c$ is graphed. The x- intercepts need to be identified from the graph and verified by substituting the corresponding values of x in the equation.

Here, since the first intercept is between $(0,0)$ and $(1,0)$ and the second intercept is between $(2,0)$ and $(3,0)$ . We will have to estimate the solution.

All values between the pair of points are taken with an increment of 0.1. The value closest to 0 is considered from the values in the table.

  $-x^2+3x-1=0$

For intercept between $(0,0)$ and $(1,0)$ .

x	y
0.1	-0.71
0.2	-0.44
0.3	-0.19
0.4	0.04
0.5	0.25

Therefore, $x=0.4$ is taken as the approximate solution for the given equation as the value corresponding is the closest to 0.

For intercept between $(2,0)$ and $(3,0)$ .

x	y
2.1	0.89
2.2	0.76
2.3	0.61
2.4	0.44
2.5	0.25
2.6	0.04
2.7	-0.19

Therefore, $x=2.6$ is taken as the approximate solution for the given equation as the value corresponding is the closest to 0.