Class notes
Lecture notes
- Course
- 201-015-RE
- Institution
- Dawson College ( )
Lecture notes of 8 pages for the course 201-015-RE at (Sec v math)
[Show more]
Seller
Follow
Content preview
Quadratic EquationsDef : An
-
equation of the form aX2tbxtc=0 where
a. b. & C are real ribs L w/ a 0) is a
"
quadratic equation =
[ form
"
in standard .
-
A quadratic equation will have :
* 2 solutions
lil if b? Uac > 0 ( Xi & ✗ a) ,
*
Lii) ( Xi
1 solution ✗ 2=4) if 62 Hae so = -
,
* Liii ) no solutions if 62 Uac < 0 ,
-
-
There are 3
major techiqeus for solving quadratic equations :
2
i
factoring
Quadratic formula } ( Most common)
3
Square
-
root both sides ( special case)
-
for 1
factoring Quad form , the quadratic
& 2
equation
must be in standard form : aX2t6✗tC=O
factoring
1
-
We make use of the following FACT if A. 8=0 then ,
A- =D or 8=0 (or both )
in order to solve
eq a✗ʰtbXtc -0
a quad , by factoring
the
left -
hand side &
setting the factors = to
,
0 to solve fork
the equation ✗21-7 ✗
-
Eg : Solve -10 =
first, ✗21-7×1-10=0
→
put it in standard form :
Then
, factor the LHS (✗ 1- 2) 1×+51=0 LHS : Left
This implies that
{ Kt 2=0 ✗ t 5 = 0 ✗
✗ =
=
-2
-5
hand side
Solve ✗2=4×-4
-
Eg :
✗2- 4×+4=0 ( binomial squared )
1×-211×-21=0 or 1×-212=0
so
,
{ ✗ -2=0 ✗ 2 =
, ✗ 21-1=0 V. 8 : ✗ 2=-1
Eg No Solve
solution
:
5×2 = Fi
-
for ✗ 21-1=0 ✗ = if
a = 1
,
6=0 ,
Csl
so 62 Uac so -44 )(1)
-
= -4<0
Eg : Solve the equation ✗ 3-94=0
{ x=◦ ×=
-
✗ 3-94=0
✗ 1×2-91=0 X -
3=0 ✗ =3
✗ 1×-331×+31=0 .
}
Solve for the
Eg :
lengths of the sides of the right triangle below
e
✗+ "
✗ +2 Recall : Pythagorean theorem
b
c%a762
a
DO ,
1×1-412=1/21-1×+212
✗
✗ 21-8×1-16 = ✗21-1174×1-4=2×21-4×+4
0=2×21-4×+4 -
✗ 2-8×1-16
◦
0=(11-611×1-2)
= ✗ 2-4×-12 →
{ ×
✗ +2=0
-6=0 11=6
✗ = -2
Reject
lengths
this since
can't be -
ve
=) The side
lengths are 10
g
6
-
Exercises :
1 Solve the equation
a. ✗ 2-4×+3=0 b. ✗ 2=511
C. 16×2-49=0 d- 2×2-8×-3=0 e. ✗ 3=10×4-3911
2 If -1 is one solution of ✗ 21-4×1-5=0
find the other one .
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller gland_mack0m. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$11.84. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
56326 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now