2.2 Solving Quadratic Equation
A quadratic equation can be solved by using:
1. Factorization
i) Arrange the unknowns in general form (ax2+bx+c=0) and factorize it 2. Completing the square
i) x2-6x+4=0
ii) x2-6x=-4
iii) x2-6x+-622=-4+-622
iv) x2-6x+-32=-4+-32
v) x-32=5
vi) x-3=±5
vii) x=3±5
viii) x=3+5 OR 3-5
ix) x=5.236/0.7369

3. Quadratic formula
x=-b±b2-4ac2a
* Forming quadratic equation from given roots
SOR=sum of roots POR=product of roots
SOR=-ba POR=ca
.x2-α+βx+αβ=0
.x2-SORx+POR=0
* Types of roots
b2-4ac>0| Two different roots| Straight line intersects a curve at two different points| b2-4ac=0| Two equal roots| Straight line touches the curve at one point/ tangent to the curve| b2-4ac<0| No real roots| Straight line does not intersect the curve|

Example Questions:
1. Show that the quadratic equation x2=21-kx-9-k2 has two real roots for k≤-4. Solution:
.x2-21-kx+9+k2=0
.a=1, b=-2+2k, c=9+k2
Since it has 2 real roots,
.b2-4ac≥0 {It didn’t mention that the 2 roots are equal roots or different roots, so it can be >0/=0 that becomes ≥0} .(-2+2k)2-4(1)(9+k2)≥0
.4-8k+4k2-36-4k2≥0
.-8k-32≥0
.-8k≥32
.-k≥4
.k≤-4 (shown)

...Non organelle
b) Non organelle
Characteristics
Functions
1. Plasma/cell membrane
-made of_________ & phospholipids
-________ permeable
-it regulates the_______of substances_____and out of the cytoplasm
2. Cell wall
(Plant cell)
-made of _________.
- _______ to all fluids
-gives _____ to plant
-provides mechanical ________ for the plant cell
3. Cytoplasm
-jelly-like matrix
-medium which organelles are _______.
-contains organic and inorganic substances...

...students.
2 To calculate BMI of each students.
3 To represent data using various methods.
4 To relate students’ knowledge with the data obtained.
5 To suggest ways to practice healthy lifestyle.
The methods of research are as follows:
1 To obtain the height, weight and BMI of 50 students in Form 1 and 50 students in Form 5.
2 To tabulate the data consisting the height, weight and BMI of this 100 students.
3 To...

... Caribbean
Examinations
Council
All
rights
reserved.
No
part
of
this
publication
may
be
reproduced,
stored
in
a
retrieval
system,
or
transmitted
in
any
form,
or
by
any
means
electronic,
photocopying,
recording
or
otherwise
without
prior
permission
of
the
author
or
publisher.
Correspondence
related
to...

...ECO 550 WEEK 2CHAPTER 3 AND CHAPTER4 PROBLEMS
download here
Chapter 3: Problems 3, 4, and 7
3. The Olde Yogurt Factory has reduced the price of its popular Mmmm Sundae from $2.25 to $1.75. As a result, the firm’s daily sales of these sundaes have increased from 1,500/day to 1,800/day. Compute the arc price elasticity of demand over this price and consumption quantity range.
4. The subway...

...20
Additional Mathematics
Project Work 2
Written by: ALVIN SOO CHUN KIT I/C Num : Angka Giliran: School : Date :
Alvin Soo Chun Kit
Additional Mathematics Project Work 2
2011
TABLE OF CONTENTS
Num. 1 Part I Part II ~ Question 1 ~ Question 2 (a) ~ Question 2 (b) 2 ~ Question 2 (c) ~ Question 3 (a) ~ Question 3 (b) ~ Question 3 (c) 3 4 Part III Further Exploration Question Page...

...Case # 4Chapter2.
Issue: There are two parties involved in the case dispute the one is called plaintiff, according to Kubasek. , Browne, , Herron, , Giampetro-Meyer, , Barkacs, , Dhooge, , & Williamson, (2012) the definition of plaintiff is, “ the person or party who initiates a lawsuit (an action) before a court by filing a complaint with the clerk of the court against the defendant(s). Also known as claimant or complainant,” (page, G22). In...

...Student ID: 22087885
Exam: 986093RR - Business Math, Part 2
1. Ann works 51/2 hours, Mary works 61/3 hours, and John works 41/4 hours. How many combined hours
have they worked?
A. 165/12
*B. 161/12
C. 151/12
D. 155/12
2. You pay the following for supplies: $19.36 for pens; $21.75 for notepads; and $32.26 for computer
paper. What is your total?
A. $73.73
B. $77.37
C. $77.73
*D. $73.37
3. How many liters will a U.S. 6-quart...

582 Words |
3 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":37058425,"categoryName":"Literature","categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":2,"pageRange":"1-2","totalPages":2}},"access":"premium","title":"Form 4 Add Math Chapter 2","additionalIds":[],"additional":[],"loadedPages":{"html":[],"text":[1,2]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Form-4-Add-Math-Chapter-2-1427665.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"},"analytics":{"googleId":"UA-32718321-1"}}