Chapter 9, Problem 10PT

To determine

To solve equation by graphing

Answer to Problem 10PT

  $x=-2,-5$

Explanation of Solution

Given information :

The function provided is $x^2+7x+10=0$

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, the intercepts as seen in the graph are $(-2,0)$ and $(-5,0)$ .

The original equation is.

  $x^2+7x+10=0$

Substituting the value of x as $x=-2$ ,

  ${(-2)}^2+7(-2)+10=0$

Simplifying.

  $4-14+10=0$

Therefore, since the right hand side of the equation is equal to left hand side, the identified x- intercept is a solution for the graph.

Similarly,

Substituting the value of x as $x=-5$ ,

  ${(-5)}^2+7(-5)+10=0$

Simplifying.

  $25-35+10=0$

Therefore, since the right hand side of the equation is equal to left hand side, the identified x- intercept is a solution for the graph.