Chapter VI

In this chapter, students will be taught how to find solutions to quadratic

equations. This lesson assumes students are already familiar with solving simple

quadratic equations by hand, and that they have become relatively comfortable using

their graphing calculator for solving arithmetic problems and simple algebra problems.

Students will also be shown strategies on how to use the keys on the graphing

calculator to show a complete graph.

TARGET SKILLS:

At the end of this chapter, students are expected to:

• use calculator in solving quadratic equation;

• solve equation on a calculator; and.

• improve skills using calculator by solving quadratic equation.

Lesson 15

Equation on a Calculator OBJECTIVES:

At the end of this lesson, students are expected to:

acquire knowledge using calculator in solving quadratic equation;

resolve equations on a calculator; and

improve skills on solving quadratic equation using a calculator.

The simplest way to solve a quadratic equation on a

calculator is to use the quadratic formula.

X=-b ± √d where d=b² - 4ac

2a

As we have seen, if d < 0, there are no real solutions. But f d ≥ 0, then

we can use calculator to get the solutions.

To solve 3x² + 5x – 7 = 0, first compute the discriminant.

d = b² - 4ac = 5² - 4(3)(-7).

On an arithmetic calculator, the keystroke sequence for d is,

[AC][MC] 4 [x] 3 [x] 7 [=][M+] 5 [x][=][+][MR][=]

The display will show the value of the discriminant to be 109, and so the

quadratic equation has two distinct roots. To compute the roots, proceed

as follows:

[AC][MC] 109 [√][M+][MR][-] 5 [+] 2 [x] 3 [=] the first root and

0 [-][MR][-] 5 [+] 2 [ x] 3 [=] the second root.

On an algebraic calculator, the keystroke sequence is easier. Recall that

the actual roots are:

x= -5 + √5 ²−4 (3)(−7)

2(3)

x= -5 -√5 ²−4 (3)(−7)

2(3)

First, we compute the square root of the discriminant and store it is

memory.

[AC] 5 [2] – 4 [x] 3 [x] 7 [+/-][=][√][Min]

Then, compute the first root as:

x1 = (5 [+/-][+][MR])[÷] (2 [x] 3) [=];

and then compute the second root as:

x2 = (5[+/-][-][MR])[+] (2 [x] 3)[=].

Exercise:

Find the roots of the following equations.

1. 3.5x2 + 1.2x – 3.2 = 0

2. 7.6 -2.2x – 1.7x2 = 0

3. 2.5x2 + 5.6x – 13.5 = 0

4. x – 77.3 + 2.3x2 = 0

5. x2 - 1000.5 + 32.3 = 0

Name: ___________________ Section: _______

Instructor: ________________ Date: _______ Rating: ____

Instruction: Find the roots o the following equations.

1. 5.3x2 + 2.1v – 2.3 = 0

_____________________________________________________

2. 6.7 v - 2.2x – 7.1x2 = 0

_____________________________________________________

3. 5.2x2 + 6.5x – 5.13 = 0

_____________________________________________________

4. x2 – 50.001 + 33.2 = 0

_____________________________________________________

5. x – 7.73 + 2.3x2 = 0

____________________________________________________

6. 3.3x2 – 1.9x – 7.10 = 0

_____________________________________________________

7. 3.1x – 9.1x2 – 7.10 = 0

_____________________________________________________

8. 6.3x2+ 8.5x = 9.5

_____________________________________________________

9. 5.9x – 9.5x2 = 8.03

_____________________________________________________

10.3.2x2 + 2.3x = 23.32

_____________________________________________________

11.9.9x – 7.7x2 – 8.8 = 0

_____________________________________________________

12.6.3x + 5.3x2 – 3.4 = 0

_____________________________________________________

13.6.3x2 – 2.9x – 8.10 = 0

_____________________________________________________

14.3.4x – 8.1x2 – 4.10 = 0

_____________________________________________________

15.6.2x2 + 3.6v – 3.7 = 0

Instruction: Find the roots o the following equations.

1. 5.3f2 + 2.1f – 2.4 = 0

2. 6.7 x - 2.2x – 8.1x2 = 0

3. 5.2r2 + 6.5r – 5.13 = 0

4. s2 – 50.001 + 33.2 = 0

5. g – 7.73 + 2.3g2 = 0

6. 3.3o2 – 1.9o – 7.10 = 0

7. 3.1e – 9.1e2 – 7.10 = 0

8. 6.3r2+ 8.5r = 9.5

9. 5.9i – 9.5i2 = 8.03

10.3.2o2 + 2.3o = 23.32

11.9.9p – 7.7p2 – 8.8 = 0

12.6.3h + 5.3h2 – 3.8 = 0

13.6.3x2 – 3.9x – 8.10 = 0

14.3.4x – 9.1x2 – 4.10 = 0

15.5.2v2 + 3.6v – 4.7 = 0