Question

In ax5+bx4+cx3+dx2+cx+f=0ax5+bx4+cx3+dx2+cx+f=0  if (a+c+e)=(b+d+f)(a+c+e)=(b+d+f) , then factor of f(x)f(x) is​

Answer 1

Given : ax⁵+bx⁴+cx³+dx²+ex+f=0

(a+c+e)=(b+d+f)

To find : factor of f(x)

Solution:

ax⁵+bx⁴+cx³+dx²+ex+f=0

put x = - 1

=> a(-1)⁵+b(-1)⁴+c(-1)³+d(-1)²+e(-1)+f=0

=> -a  + b - c  + d  - e + f = 0

=> b + d + f = a + c + e

as Given

Hence x = - 1  

x + 1 = 0

Hence x + 1 is a factor  of  ax⁵+bx⁴+cx³+dx²+ex+f

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