Quandaries and Queries


Who is asking: Student
Level: Secondary

|ax+b| = cx + d

how to show sometimes the above has 2 roots, sometimes 1 root and sometimes no roots. Hopelessly lost on how to start...

so far I have
1. ax+b = cx+d
2. -ax-b = cx+d

using 1.
x = (d-b)/(a-c)

using 2.
x= -(d+b)/(a-c)

please help



Hi Angel,

I think your teacher is looking for values of a, b, c and that will give 1 root, 2 roots or no roots.

For example if a = 1, d = 1 and b = c = 0 then the equation becomes

|x| = 1

In this situation x can be 1 or -1 and thus this is a situation with 2 roots.

Can you find choices for a, b, c and that will give no roots? 1 root?



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