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Omni-MATH / The degrees of polynomials P and Q with real coefficients do not exceed n. These polynomials satisfy the identity P(x)x^(n+1)+Q(x)(x+1)^(n+1)=1. Determine all possible values of …

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problem

The degrees of polynomials PP and QQ with real coefficients do not exceed nn. These polynomials satisfy the identity P(x)xn+1+Q(x)(x+1)n+1=1. P(x) x^{n + 1} + Q(x) (x+1)^{n + 1} = 1. Determine all possible values of Q(−12)Q \left( - \frac{1}{2} \right).
Plain-text mathematical notation (without MathML)
The degrees of polynomials P and Q with real coefficients do not exceed n. These polynomials satisfy the identity
P(x)x^(n+1)+Q(x)(x+1)^(n+1)=1.
Determine all possible values of Q(−(1)/(2)).
Original LaTeX notation
The degrees of polynomials $P$ and $Q$ with real coefficients do not exceed $n$. These polynomials satisfy the identity
\[ P(x) x^{n + 1} + Q(x) (x+1)^{n + 1} = 1. \]
Determine all possible values of $Q \left( - \frac{1}{2} \right)$.

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task_id
f1715946-b429-55dd-994c-c7ddf43cc589
task_key
test--f1715946-b429-55dd-994c-c7ddf43cc589
task_revision_id
1
config / split
/ test

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