Chapter 9.3, Problem 43HP

To determine

To calculate the roots of the given equation.

Answer to Problem 43HP

The roots of the given equation are $+1.5$ and $-1.5$ .

Explanation of Solution

Given information :

The equation provided is $x^2=2.25$ . This can be written as a quadratic equation as $x^2-2.25=0$ .

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.

To cross check, put these values in the given equation to confirm that the left-hand side and right-hand side matches.

Calculation :

The graph of the given equation is

  

In this, the parabola has x-intercept at $\left(-1.5,0\right)$ and $\left(1.5,0\right)$ .

Now, cross check by putting these values of x-coordinate in the given equation.

  $x^2-2.25=0$

This is the given equation.

  $=>{\left(-1.5\right)}^2-2.25=0$

Putting $x=-1.5$

  $=>2.25-2.25=0$

Simplifying this

  $=>0=0$

  $=>{\left(1.5\right)}^2-2.25=0$

Putting other root, $x=1.5$

  $=>2.25-2.25=0$

Simplifying this

  $=>0=0$

Thus the test is a success and the result is $x=\pm 1.5$ .