mum_sugoku:

bran36:

Hi, as the exams are near, I'm preparing for my papers. However, while doing my assessment book, there's this question I do not understand.

It's an inequality question. I don't understand why must the sign change. Perhaps anyone can enlighten me? Many thanks!!

My work:
http://i44.tinypic.com/2gxfqdv.jpg

The Answer:
http://i44.tinypic.com/35irdbp.jpg

(Actually it's quite hard to explain without using drawings but let me try )

First of all, the eqn you have is a quadratic eqn (ie eqn in the form of ax^2 + bx + c) which, if you were to draw a graph of the eqn, it's either a U shape curve (if a is +ve), or an inverted U (if a is -ve).

Next, if we look at your eqn x^2 -4x +3 >=0, or (x-3)(x-1)>=0
since a (ie coef of x^2) is = +ve, it's a U shape curve which cuts the x-axis (ie y=0) at x=3 and x=1

What it means is that when x is between 1 and 3 (ie 1<x<3) the curve falls below the x-axis (ie eqn is -ve), and when x is <1 and when x is >3, the curve rises above the x-axis (ie eqn is +ve).

Hence for eqn to be >= 0 (ie +ve), x<1 or x>3.

If you can't understand the above explanation, alternatively, just bear in mind that for quadratic inequality eqn, say (x-3)(x-1)>0, ans is always either in the form

1<x<3, or

x<1, or x>3

To find out which is the correct ans, one way is to pick a number between 1 and 3, say x=2, and insert into the eqn, and you'll get (2-3)(2-1) = -1, which is <0. Since question ask for >=0, correct ans has to be the second one, ie x<1 or x>3.

Hi thanks a lot for your help! However, how do you which value of x is > or <? I don't really understand this part. Thanks again!

Hi, as the exams are near, I'm preparing for my papers. However, while doing my assessment book, there's this question I do not understand.

It's an inequality question. I don't understand why must the sign change. Perhaps anyone can enlighten me? Many thanks!!

My work:
http://i44.tinypic.com/2gxfqdv.jpg

The Answer:
http://i44.tinypic.com/35irdbp.jpg

Hi guys, I will be taking my 'O' levels this year and I need some assessment books or guide books to improve on my following subjects;


1) Additional Maths
2) Elemetary Maths
3) English
4) Science (Combined Chem and Phy)

My grades are so-so, with B3 and above for all the above mentioned subjects except for english with a C5. I only do daily homeworks that my teacher provides me and when the exam are near, I do certain question on the TYS. Please advice me! Thanks!