O-Level Additional Math

[OK Lor]

Hi Guan Hui,


Please help to solve:

x²-286x+c=0 has roots a²b and ab². x²+px+q=0 has roots a and b. Find p and q, given that a, b and c are integer positive.

Thanks.

[Guan Hui]

if x²-286x+c=0 have root a²b and ab²

means
(x-a²b)(x-ab²)=0
expand it
x²-ab²x-a²bx+a^3b^3=0
x²-(ab²+a²b)x+a^3b^3=0
so…
ab²+a²b=286------1
a^3 b^3=c---------2

x²+px+q=0
(x-a)(x-b)=0
x²+x(-a-b)+ab=0
-a-b=p--------------3
ab=q----------------4



ab²+a²b=286
ab(a+b)=286
since a b and c are integer positive
ab and (a+b) are integer positive
factors of 286
1x286
2x143
11x26
13x22

13=(11+2) while 22 =(11x2)
a=11 or 2 and b=2 or 11
c= a^3b^3=11^3 2^3
c=10648

p=-a-b
p=-13
q=11x2
=22

sorry for late answer just saw it this morning.

[OK Lor]

Hi Guan Hui,


Thanks a lot, cheers.

[Muffins]

Hey Guan Hui, Secondary version of Mathsguru!

[Guan Hui]

Muffins:

Hey Guan Hui, Secondary version of Mathsguru!

I am so flattered haha=) Just glad i can do something for this awesome community.

[Muffins]

Hey, don't ever forget, you are part of this awesome community!

[Guan Hui]

I am glad

[starlight1968sg]

This is wonderful; we have a tutor for secondary school maths.

Thanks guanhui.
I beg your pardon :oops:

[Guan Hui]

I am just glad I am of some help. It help to expose me to more difficult question that I can give my students anyway.


The parents here give tough questions=D

[Muffins]

and the kids give even tougher questions!