Question

if a+c+e=0 and b+d=0 prove ax⁴+bx³+cx²+dx+e is divisible by x²-1​

Answer 1

Step-by-step explanation:

If the given equation is divisible by

${x}^{2} - 1$

then, at x=1 and x=-1, the equation becomes equal to zero.

At x=1,

$a + b + c + d + e = 0$

At x=-1,

$a - b + c - d + e = 0$

Adding both of these equations, we get

$a + c + e = 0 = b + d$

Hence verified

Thank you