VCE Methods Question Thread!

[BubbleWrapMan]

Not really, you seem to understand what a polynomial is, it's just non-negative integer powers of the variable (usually ), multiplied by constants and added together. Basically you just need to be able to recognise them, you won't be tested on definitions.

[Only Cheating Yourself]

Not really, you seem to understand what a polynomial is, it's just non-negative integer powers of the variable (usually ), multiplied by constants and added together. Basically you just need to be able to recognise them, you won't be tested on definitions.

Ok, so you've got linear polynomials which are a degree of 1?  Quadratic polynomials which are degrees of 2-power of of2 2? cubic polynomials which are degree of 3 and quartic polynomial which are degree of 4-the power of 4 same thing?  This bring me to a question, if you don't mind me asking.  In year 10 we never learnt quadratics etc, and in methods i've self taught quadratic polynomials etc, but if i want to solve for x for a linear equation which isn't just x(degree of 1) i would just get x on one side and rest on the other to solve for x, but when you're dealing with quadratic polynomials i don't think you're able to that?  Because you can't have x^2 =….. So this is where i can use fixed point iteration?  This is why i made a thread on thinking like mathematician, not getting cocky by any stretch of the imagination but i think i'm starting to learn the concepts rather than have memorised answers etc… Not sure though, only time will tell if i'm correct.

[brightsky]

For quadratics, just complete the square.

[Only Cheating Yourself]

For quadratics, just complete the square.

what?  don't i use cts if inspection fails?

[BubbleWrapMan]

It doesn't matter what method you use, so it's better to use what you're comfortable with. Completing the square covers all cases of quadratics though. The quadratic formula basically comes from completing the square; you should try and prove the formula yourself.

[Only Cheating Yourself]

It doesn't matter what method you use, so it's better to use what you're comfortable with. Completing the square covers all cases of quadratics though. The quadratic formula basically comes from completing the square; you should try and prove the formula yourself.

This is what i mean i don't get this!  How come you guys say use cts for quadratics but there are like 5 methods of factorising?  How can you use CTS for all quadratics?

[BubbleWrapMan]

Well... try it? Solve something like by completing the square and also by factoring. Factoring is useful when the factorisation is 'obvious', but you can complete the square for the same thing. If you can factor it easily then completing the square just isn't very efficient, but you can still do it.

[Only Cheating Yourself]

Well... try it? Solve something like by completing the square and also by factoring. Factoring is useful when the factorisation is 'obvious', but you can complete the square for the same thing. If you can factor it easily then completing the square just isn't very efficient, but you can still do it.

When ever i get a quadratic equation that is a trinomial i always first look for inspection.  Then if thats doesn't work i do cts.  But to answer that question

1.) Using inspection i got (x+2)(x-3)

2.) Using cts i got( x-1/2x-square root 7)(x-1/2x+square root 7)

?

[BubbleWrapMan]

You should be getting the same answer, show your working?

Also, this is nitpicky, but your answers should be "", rather than factorisations, since you're asked to solve an equation. You'd get marked down for this sort of thing.

[Only Cheating Yourself]

You should be getting the same answer, show your working?

Also, this is nitpicky, but your answers should be "", rather than factorisations, since you're asked to solve an equation. You'd get marked down for this sort of thing.

My bad…

using inspection i get (x+2)(x-3) so x+2=0, x=-2 or x-3=0, x=3 so using inspection i get (-2,3)

Using completing of two square (cts) i get
x^2-x-6=0
x^2-1/2x+1/2^2-1/2^2-6
x^2-1/4-1/4-6
(x-1/2)^2 -25/4 which can be simplified to -5/2
(x-1/2-square root 5/2)(x-1/2+square root 5/2)
x-1/2-square root 5/2=0
x=1/2+5/2
x=square root 3
or
x-1/2+square root 5/2=0
x=-5/2+1/2
x=square root -2

so (3,-2)

So cts and inspection both do work, but theres one problem my answer is square root -2 and 3 not just by its self??

But CTS was too much of a hassle to be honest to many fractions etc….

[BubbleWrapMan]

You square rooted the 5 twice - you went from 25/4 to √5/2.

[Only Cheating Yourself]

You square rooted the 5 twice - you went from 25/4 to √5/2.

Yea i know i simplified it.

[BubbleWrapMan]

No, I mean √(25/4) = 5/2, not √5/2.

[Only Cheating Yourself]

No, I mean √(25/4) = 5/2, not √5/2.

Really?  Thanks for that, so when ever you simplify something in a square root it cancels the square root?  So as you can see for me inspection was easier and cts took me like 5 goes to do cause the fractions was to big and i needed to be precise so what do you suggest i use?  Also if a question was asked as a trinomial in the form of a quadratic expression but had no =0 could i still use cts and would it still be the same answer if i used inspection?

[Nato]

Hey, i just wanted to know what are the best ways to do transformations: the x',y',arrow way of using the so called 'function method"?


thanks in advance