Notes(F4:Chp1,2&6;F5:Chp3) & MSpwrpnt (Ceramah MT SPM) [By Mr Teo Poh GC]

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[Announcements] [Introduce Yourself] [ICT] [Prasekolah] [LINUS] [KSSR] [UPSR] [PMR] [SPM] [STPM] [School] [Classroom] [Clubs & Uniformed Bodies] [JPN] [SPA] [SICT] [SPP] [SPS] [SPPK] [SPSPK] [SPI] [SPsK] [JNJK] [PPD] [Program] [Computer & Internet] [Let's Hear It From You] [Membergroup]

[Lim Yu Teong]

Hi,
Attached with this mail are five files.

[Angela Choi]

Dear Mr Teo,
I find your notes and exercises very informative and well graded.  I have downloaded them for further reference.  Thank you for sharing your hard work with us.  Thank you very much.

from
angela

[Fiona Toh]

Thank you for the notes MR. Teo. I don't know how to teach my sister Additional maths so, your notes have been very useful and helpful for us. thank you.

[Idrin Lee]

Dear Mr. Teo,
   
   Thank You so much for the notes!! Can you give me the notes from Chapter 3, 4, 5, 7, 8, 9, 10, 11 (Form 4) and the other chapter from Form 5?? Thanks A Lot!!

[Kong Chung Teck]

Thanks a lot Mr. Teo

   The notes and exercises help my students a lot!! Do you have notes and exercises from other Chapters??

[Anne Lee]

Thanks for ur information.
It really save my time.
God Bless..

[Christopher Hii]

Thanks a lot, : )

[Lina Fung]

Thanz A lots..

[Susan Chow]

Mr. Lim,
   Thank you for posting the useful materials.  I have downloaded your powerpoint that you have mentioned.  Thanks so much.

[Law Siao Siu]

thank u Mr Lim & Mr Teo!

[Crispin Tan Phong Leng]

Mr.Lim,

Chapter 2 Quadratic Equation

L10(c) Prove that the roots of the equation (1 – p)x² + x + p = 0 are real and negative   
          IF 0 <  p  <  1.                                         
 
how to prove it 
Sorry for disturbing you 

[Norhafizan]

tq for sharing
have a nice day

[Liew Teck Hui]

Thanks for sharing....Have a nice day!!! 

[Norlina Kamin]

Thank you sir.

[Lee Bin Saat]

Tq....for sharing.

[Jason Lee]

Thanks for sharing 

[Lee Siew Yuh]

Thank you, Mr. Lim.

[Dominic Tan Kuan Yew]

Thanks, give u a fame.

[Wilter Hawell]

Terima Kasih Mr Lim

[Wong Tok Hua]

Crispin,

If the roots of the equation are real, then b² – 4ac > 0
(1)² – 4(1 – p)(p) > 0
1 – 4p + 4p² > 0
4p² – 4p + 1 > 0
(2p – 1)² > 0
So, it is true for all real values of p.

If the roots are negative, then sum of roots is negative and the product of roots is positive

Sum of roots = -(1/(1-p)) < 0
                       1/(p-1) < 0
Therefore, p-1 < 0 and p < 1.
Product of roots = p/(1-p)>0
Assuming (1-p) is not zero, p > 0

So, if the roots are real and negative, the range of p should be
0 < p < 1.

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