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Quadratic Equation - Turn Problem Sum to Solution Sum

**Question**

Pauline has two brothers, Peter and Philip. Pauline is x years old. Peter is 3 years older than Pauline. Philip is 2 years younger than Pauline.

a) Given that the product of the two brothers is 126 years, show that x^2 + x - 132 = 0.

b) Solve the equation to find the ages of the three children.

**Strategies of solving Problem Sum**

**"Break into Pieces"**

"Pauline is x years old" -> Pauline: **x **

"Peter is **3 years older** than Pauline -> Peter: **x** **+ 3**

**NOTE:** You just** Link** the Pauline's age to Peter's age, u will know Peter's actual age

You need to so-called rephrase English language to Maths Expression(**Modification**)

"Philip is **2 years younger** than Pauline." -> Philip: x**-2**

**NOTE**: You need tobreak out into 3 sentences.

Understand sentence by sentence("Break Into Pieces").

**Link** one another if possible.

**Transformation(Name to Algebra)**

"...**product** of the two brother.." -> Peter *** **Philip

= (x+3) * (x-2) ; Tranformation:Name to Eqn

= x^2 - 2x + 3x - 6 ; Modification: Expansion

= x^2 + 3x - 2x - 6 ; Modification: Arrangement

= x^2 + x - 6 ; Combination: Comine 3x -2x to be x

**NOTE:** Form equation > **Arrange** x wif x, No. wif No. > **Combine**: 2x + 1

"...**is** 126." -> x^2 + x - 6 **=** 126

**Modification **using the Power of **BALANCE**: x^2 + x - 6 - 126 = 126 - 126

x^2 + x - 132 = 0 (shown)

"Solve..." means to find unknown x

Since it is Qudratic Eqn, therefore you should use General Formula

(See How powerful "Question is the Answer")

------------------- ----------------- SUMMARY ------------------------------------------

1. Question is the Answer - you don't need to memorize. Just SEE and Do it!

2. Break Into Pieces - for clearer interpret, therefore better understanding

3. Transformation - Sentence to a 'Picture' form for anlayzing clearly

4. Modification - do a powerful presentation

5. Combination - combine whatever info you have understand after 'break into pieces'

6. Linking - Link up all present info that you have just combined and bring your PAST

(what you have learnt) to link to the present information!

------------------------------------- SUMMARY -------------------------------------------

**FeedBack to me how I can make this blog better and How I can 'cure' your Maths Hatred!**

Proudly done by Mr K L CHUA

- the founder of Maths Specialist

- the creator of FiloMaths

- http://www.filomaths.com

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