Q : If a, b and c IR , with a is not 0 , and the roots of the equation are real , show that the roots of are also real .
If the roots of the quadratic equation are and , state the value of and in terms of a ,b and c . Hence , find the roots of the second equation in terms of and .
I don understand this part only --- hence , find the roots of the second equation ( the last sentence )
Hello, mathaddict!
I think I understand what they want.
I don't know if I've found the shortest way, though . . .
We already know that: . . [1]If and the roots of the equation are real,
show that the roots of are also real.
If the roots of the quadratic equation are ,
state the value of and in terms of
Hence, find the roots of the second equation in terms of and
Using the Quadratic Formula on the second equation,
. . we have: .
We will now manipulate this expression beyond all recognition . . .
We have: . .
. . . . . . . . . [2]
Substitute [1] into [2]:
. .
. .
. .
. .
Therefore: .
The simplicity of these answers leads me to suspect that
. . there is a more direct approach.
So far, I haven't found it . . . anyone? anyone?
Edit: Too fast for me, Danny!