Hello,Originally Posted by nath_quam
all your results are correct. (Congratulations!)
with g): Plug in the values you know and you'll have:
with i): You may know that . With your solutions you get:
Greetings
EB
This is for anyone who wants a challenge with polynomials because they are too difficult for me thank you for any help
i have found the answers
a)-2
b)-11
c)12
d)-11/12
e)-1/6
f)0
g)-132
h)26
i)13/72
would someone be able to check these
Hello, nath_quam!
These are great problems!
They give me a chance to show-off . . . LOL!
The first three are easy . . . if you know this theorem:
If are roots of the cubic
. . then: .
If are roots of , find:
Then it gets interesting!
These problems lend themselves to some clever manipulations.
. . . . .
. . . . .
. . . This one requires Olympic-level gymnastics.
We know that: .
. . . . Hence: .
Expand: .
We have: .
Hence: .
. . . . .