Chapter 9.2, Problem 46HP

To determine

Explain how to approximate the roots of quadratic equation when the roots are not integers.

Answer to Problem 46HP

The zeros of the equation $x^2-1.25=0$ are about $1.2\text{and}-1.2$

Explanation of Solution

Given:

Concept Used:

First graph the related function. Then determine between which two integers the graph crossed the x axis. Make a table going by tenths of the values between the integers. Locate where the function values changes signs.

The x − value for which the functions value is closest to zero is the beast approximation of the root of the equation.

Calculation:

Consider the quadratic equation: $x^2-1.25=0$

The zeros are between − 1 to − 1.3 and 1 to 1.3 x y=x2 – 1.25 x y=x2 – 1.25 1 – 0.25 – 1 – 0.25 1.1 – 0.04 – 1.1 – 0.04 1.2 + 0.19 – 1.2 + 0.19 1.3 + 0.44 – 1.3 + 0.44 The zeros are about $1.2\text{and}-1.2$

Thus, the zeros of the equation $x^2-1.25=0$ are about $1.2\text{and}-1.2$