IF X2+1 IS A FACTOR OF AX4 + BX3 +CX2+DX +E

THEN SHOW THAT A+C+E=B+D=0

Asked by vrishti TOKAS | 9th Jun, 2015, 08:15: PM

Expert Answer:

The correct factor for the given polynomial should be x2-1 . Please check the question. Assuming the factor to be x2-1, we proceed as follows:
Since x2-1 is a factor of f(x)=Ax4+Bx3+Cx2+Dx+E, by factor theorem , f(a)=0, where 'a' is a root of x2-1
x2-1=0 => x=(+/-)1. Hence f(1)=0 and f(-1)=0
f(1)=0 
=> A+B+C+D+E=0.....(1)
f(-1)=0
=> A-B+C-D+E=0.....(2)
Adding (1) and (2), we get 2(A+C+E)=0 => A+C+E=0
Subtracting (2) from (1), we get 2(B+D)=0 => B+D=0
Hence, A+C+E=B+D=0 (Proved)

Answered by satyajit samal | 10th Jun, 2015, 09:33: AM

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