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For what value of ‘a’, the given equation x14 + ax10 – x8 – 2 when divided by x2 – 2 gives remainder 14?

For what value of ‘a’, the given equation x14 + ax10 – x8 – 2 when divided by x2 – 2 gives remainder 14? Correct Answer -3

Given:

Dividend = x14 + ax10 – x8 – 2

Divisor = x2 – 2

Remainder = 14

Concept:

Since, the equation is divided by x2 - 2, put the value of x2 = (2) in the equation and equate it with the remainder to get the value of a.

Calculation:

∵ x14 + ax10 – x8 – 2 = 5(x2)7 + a(x2)5 – (x2)4 – 2

Put the value of x2 = (2) in the equation;                         

∴ (2)7 + a(2)5 – (2)4 – 2 = 14

⇒ 128 + 32a – 16 – 2 = 14

⇒ 128 – 18 + 32a = 14

⇒ 110 + 32a = 14

⇒ 32a = 14 – 110

⇒ 32a = (-96)

⇒ a = (-96)/32

⇒ a = (-3)

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