Q. 243.7( 23 Votes )

# If (x^{2} – 1) is a factor of ax^{4} + bx^{3} + cx^{2} + dx + e. Then, prove that

a – b + c = d – e

Answer :

**Concept Used:**

Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0

**Explanation:**

Let f(x) = ax^{4} + bx^{3} + cx^{2} + dx + e

If (x^{2} – 1) is a factor of f(x), then (x + 1) and (x – 1) are the factors of f(x).

Therefore, f(1) = f(–1) = 0

f(1) = a + b + c + d + e = 0

f(–1) = a – b + c – d + e = 0

a + c + e = b + d

a – b + c = d – e

**Hence, Proved.**

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