Polynomial Functions

A

AdkAdi

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If for a Quadratic Monic polynomial [imath]P(x+1/x)= P(x)+P(1/x)[/imath] Find the coefficient of x?

I made two Different quadratic equations one of P(x) and the other of P(1/x) and added them, then tried some manipulations but the latter one,i.e. P(1/x) could not be a polynomial...
 
If you have defined P(t) = t^2 + bt +c, then P(x) = x^2 + bx + c.

Why have you changed the coefficients?

P(1/x) will also involve b and c.
 
You had not said previously that t = x +1/x.

I'd define P(x) = x^2 + bx + c
Find P(1/x).
Then find P(x+1/x).
Equate P(x) + P(1/x) = P(1+1/x) and compare coefficients.
 
Harry_the_cat said:
You had not said previously that t = x +1/x.

I'd define P(x) = x^2 + bx + c
Find P(1/x).
Then find P(x+1/x).
Equate P(x) + P(1/x) = P(1+1/x) and compare coefficients.
Click to expand...
I tried this . The result was that all the terms got cancelled out and I was left with an equality which stated c=2.
 
Last edited:
AdkAdi said:
I tried this . The result was that all the terms got cancelled out and I was left with an equality which stated 1=2. Lol
Click to expand...
That isn't what I found. Do you want to show your work so we can work out where you have gone wrong?
 
What was the whole original question that you were given? I disagree with their answer if the question was exactly as you said in post 1.
 
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