MATHS Q. (PLEASE HELP ME!! )

Yee Ting

2006-10-22 8:22 pm

1. Consider the polynomial ax^2 + 13x + c, where a,c are integers.
Moreover, a is greater or equal to 1 and smaller or equal to 4
c is greater or equal to -30 and smaller or equal to 30.

TASK:
Find as many as possible pairs (a,c) such that the cross multiplication method can be applied on factorization of the polynomial ax^2 + 13x + c

i.e. ax^2 + 13x + c = (mx + p)(nx + q)

Please show how you get the answers. Any strategy?

回答 (1)

ChingSze

2006-10-22 11:00 pm

✔ 最佳答案

first, A can be equal to1, 2, 3 ,4
C can be equal to -30, -29, -28, -27, ... until positive 30
first, u can sub a=1 and c= -30 into the eqt.
x^2+13x-30=0
(x-2)(x+15)=0
second, u can sub a=2 andc=-29 into the eqt.
2x^2+13x-29=0
no cross multiplication can be formed
when a=3 and c=-28
3x^2+13x-28=0
no cross multiplication can be formed
when a=4 and c=-27
4x^2+13x-27=0
no cross multiplication can be formed
then worked on the steps so on..

there are no ways for you to do this kind of q. , u must try everyone of it!
work hard!

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