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If a+c+e=0 and b+d=0, then ax^4+bx^3+cx^...

If `a+c+e=0` and `b+d=0`, then `ax^4+bx^3+cx^2+dx+e` is exactly divisible by
(1)   `x+1`       (2)  `x-1`
(3)   Both (1) & (2)       (4)   None of these

Text Solution

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f(x)=ax^4+bx^3+cx^2+dx+e
f(1)=a+b+c+d+e
f(1)=0+0=0
f(x) is divisible by (x-1)
f(-1)=a(-1)^4+b(-1)^3+c(-1)^2+d(-1)+e
f(-1)=a+c+e-b-d
f(-1)=0-0=0
f(x) is divisible by (x+1)
...
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