P.S. O-Level students are advised not to be alarmed by the *chim* concepts presented in Comment #9, for you'll ONLY be dealing with *two* roots in your exam - so just focus on the stuff in the orange boxes within the main blog post.

P.P.S. The typo mentioned in Comment #6 has been fixed. Miss Loi was *really* sick when she put out this blog post (yeah yeah excuses excuses ...)

Last but not least, thanks **FoxTwo** and **Daniel** for pats pats and your well-wishes. The sneezing has completely stopped now 😀

because it helps me to remember the general form of Vieta's forumulas

when you sum , you take the next letter b (taking alpha as the letter a), with a minus sign in front BECAUSE its an ODD number of roots, getting

when you sum , you take the next letter c (taking beta as letter b), without any minus sign in front BECAUSE its an EVEN number of roots getting

]]>and the above equation can be rewritten as:

be:

and the above equation can be rewritten as:

since

]]>Part 1

The equation is:

It's interesting that you've chosen to use additional notations i.e. letting `α`' = `α`^{2}, Σ`α`' etc. etc.

But to keep to our O-Level scope, we're dealing with *quadratic* roots (not higher order polynomials) so we're pretty sure that there'll only be *two* lonely roots `α` & `β` (somehow this reminds me of Wall-E & Eve 🙂 )

So for 4`x`^{2} - `x` + 36 = 0 with roots `α`^{2}, `β`^{2}:

Sum of roots: ----- (1) (∵ )

Product of roots: ----- (2) (∵ )

For an equation with roots :

Sum of roots:

using (1), (2) above

Product of roots: using (2) above

So the equation for part 1 is

which can also be expressed as 36`x`^{2} - `x` + 4 = 0 😉

P.S. **Someone**: These are essentially the same steps you've done but just curious on your choice of notation.

Part 2

This is key part of the working. In their haste, many students have forgotten about this expression α^{2} + β^{2} = (α + β)^{2} - 2αβ when trying to calculate α, β from the given α^{2}, β^{2} and vice versa!

(reject)

Actually you already know at this point that `αβ` cannot be negative - since is obtained from `αβ` = -3 😉

because when , is negative

The 2 equations are:

Once again this can also be expressed as: 2`x`^{2} ± 5`x` + 6 = 0 😉

Pardon me if I have any errors, I'm doing this late at night, and with NO PAPER, using latex as working. Haha

]]>**Piak:** Thanks for your fervent support *sneeze*

Right?

right?

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