i have a question to do with quadratic equations but what i'm asking isn't really about quadratics but i need to it to complete the question. basically i've been set the question factorise . i know that you have to start by multiplying -25 and 54 which gives -1350. i then have to find two numbers that multiply together to give -1350 but also add together to give -15. is there a method i should use for finding the numbers i'm looking for?
thanks
Ok you have 2 equations here .
--- 1
--- 2
From 2 , make x the subject , then we get ---3
Now we substitute 3 into 1 , we get
Solve for y , i got
When , ,
and when , ,
So there are 2 sets of values for x and y which are -45 , 30 and 30 , -45 which are the same .
So when u say x is 30 , then y will be -45 and vice versa
Hope this helps .
Hello, mark!
I would factor out a -1: .Factor: . .
I know that you have to start by multiplying -25 and 54 which gives -1350.
i then have to find two numbers with a product of -1350 and a sum of -15.
Is there a method i should use for finding the numbers i'm looking for?
. . and disregard the leading minus-sign for now.
Multiply the first and last coefficients: .
Note the sign of the last term of the quadratic: .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . If it is "+", we want a sum.
. . If it is "-", we want a difference.
We have "-", so we factor 1350 into two parts whose difference is the middle coefficient, 15.
How do we factor 1350 into two parts?
Divide 1350 by 1,2,3, . . . and keep the ones that "come out even".
. .
. . .
We want the middle term to be , so we will use
We have: .
Factor: .
Factor: .
Restore the leading minus-sign: .
The answer can also be written: .