0013 chapter vi
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Transcript of 0013 chapter vi
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