Mathematics
Find the value of 'a' if x - a is a factor of the polynomial 3x3 + x2 - ax - 81.
Factorisation
ICSE 2023
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Answer
By factor theorem,
If x - a is a factor of f(x), then f(a) = 0.
Given,
x - a is a factor of the polynomial 3x3 + x2 - ax - 81.
⇒ x - a = 0
⇒ x = a.
∴ 3a3 + a2 - a.a - 81 = 0
⇒ 3a3 + a2 - a2 - 81 = 0
⇒ 3a3 - 81 = 0
⇒ 3a3 = 81
⇒ a3 =
⇒ a3 = 27
⇒ a3 = 33
⇒ a = 3.
Hence, value of a = 3.
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