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If p(x)=x^4 - 2x^3 +3x^2 -ax …

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If p(x)=x^4 - 2x^3 +3x^2 -ax + b when divided by x-1 and x+1 the remainders are 5 and 19 respectively.. Then find the remainder when p(x) is divided by (x-2).

Posted by Nisha Arora 7 years, 6 months ago

CBSE > Class 09 > Mathematics

1 answers

V Sridhar 7 years, 6 months ago

P(1)=1^4 - 2*1^3 +3*1^2 -a*1 + b =5 (replacing x by 1 ) -------------------------(1)
again,
P(-1) = (-1)^4 - 2*(-1)^3 +3(-1)^2 -a*(-1) + b =19 (replacing x by -1 ) ---------------------------(2)

Equations (1) & (2) can be simplified as under :

-a + b = 3--------------(1)
a + b = 13 --------------(2)
from the above we get a = 5 and b = 8

so P(x) = x^4 - 2x^3 +3x^2 -5x + 8

P(2) = 2^4 - 2*2^3 +3*2^2 -5*2 + 8 = 16-16+12-10+8 =10

the remainder when p(x) is divided by (x-2) will be 10

2Thank You

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