SOLUTION: the degree of a polynomial p(x)is no larger than 3. we know that p(0)=3, P(-x)=p(x), and p(1/x)=p(x)/x2. find p(1)?

Question 467123: the degree of a polynomial p(x)is no larger than 3. we know that p(0)=3,
P(-x)=p(x), and p(1/x)=p(x)/x2. find p(1)?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let M = .
Then M + 461 = .
Subtract the top equation from the bottom equation, to get

<==>
==> 461 = 2x + 1
==> 2x = 460
==> x = 230.
Hence M = = 52,900.

------------------------------------------------------------------------------
We must have ,
p(0) = 3, p(-x) = p(x), .
Let
==> p(0) = d = 3, as given.
Now
==> a = 0 by direct correspondence of terms,
b = d, and c is some real number.
==> b = d = 3, and a = 0.
==>
Now p(x) = p(-x) ==>
==> cx = -cx ==> 2cx = 0.
Since x is not zero for all values of x in the domain of p(x), this means that c = 0.
Therefore and .
RELATED QUESTIONS
Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ (answered by Fombitz)

Find the polynomial function p(x) if it is of the second degree and p(1)=3,p(0)=-1 and... (answered by lwsshak3)

Suppose P(x) is a polynomial of smallest possible degree such that: * P(x) has rational... (answered by ikleyn)

Let p(x) be a cubic polynomial. If p(0) = 0, p(1) = 1, p(2) = 2, and p(3) = 3, then... (answered by CPhill,ikleyn,math_tutor2020)

The polynomial of degree 3, P(x) has a root multiplicity 2 at x=1 and a root of... (answered by Boreal)

P(x) is a polynomial such that: P(x + 3/2)=P(x) If P(17) = 687, find the value of... (answered by KMST)

(4 points) The joint probability mass function of X and Y is given by p(1,1)=0.45... (answered by Boreal)

4. X is normally distributed with mean 12 and standard deviation 4. (a) (3 points)Find... (answered by jim_thompson5910)

If P(x) is of degree 3, what is the degree of... (answered by ikleyn)