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Question
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
Options
a + c + e = b + d
a + b +e = c + d
a + b + c = d + e
b + c + d = a + e
Solution
As`(x^2 - 1)`is a factor of polynomial
f(x2) = ax4 + bx3 + cx2 + dx + e
Therefore,
f(x) = 0
And
f(1) = 0
\[a \left( 1 \right)^4 + b \left( 1 \right)^3 + c \left( 1 \right)^2 + d\left( 1 \right) + e = 0\]
\[ \Rightarrow a + b + c + d + e = 0\]
And
f(-1) = 0
`a(-1)^4 + b(-1)^3 +c(-1)^2 + d(-1) + e = 0`
`a - b + c - d + e = 0`
Hence, a+c+e = b+d.
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