CBSE Class 10 Answered
Let P(x) be a non zero polynomial with integer coefficients. If P(n) is divisible by n for each positive integer n, what is the value of P(0)?
Asked by vikasg13.hardware | 13 Jun, 2018, 11:46: AM
Expert Answer
P(x) is a polynomial with integer coefficient .
Let , P(x) = axⁿ + a1.x(n-1) + a2.x(n-2) ........... + an.1
P(n) is divisble by n , it means this is possible only when ,
if P(x) has no constant term .
example : P(x) = x³ + x² + x
if we put x = n
P(n) = n³ + n² + n
= n( n² + n +1) is divisible by n .
hence, P(0) = 0
Let , P(x) = axⁿ + a1.x(n-1) + a2.x(n-2) ........... + an.1
P(n) is divisble by n , it means this is possible only when ,
if P(x) has no constant term .
example : P(x) = x³ + x² + x
if we put x = n
P(n) = n³ + n² + n
= n( n² + n +1) is divisible by n .
hence, P(0) = 0
Answered by Arun | 14 Jun, 2018, 10:13: AM
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