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Mathematics

Find the value of a, if (x - a) is a factor of the polynomial 3x3 + x2 - ax - 81.

Factorisation

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Answer

Let, f(x) = 3x3 + x2 - ax - 81.

Factor :

⇒ x - a = 0

⇒ x = a.

Since (x − a) is the factor, thus f(a) = 0.

⇒ 3(a)3 + a2 - a(a) - 81 = 0

⇒ 3a3 + a2 - a2 - 81 = 0

⇒ 3a3 - 81 = 0

⇒ 3a3 = 81

⇒ a3 = 813\dfrac{81}{3}

⇒ a3 = 27

⇒ a = 273\sqrt[3]{27}

⇒ a = 3.

Hence, the value of a = 3.

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