Question

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IIT based Question!

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If the remainder R(x) = ax + b is obtained by dividing the polynomial x^100 by the polynomial x² - 3x + 2 then, find the value of a and b.

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Answer 1

Answer :-

→a = ( $2^{100}$ - 1) and b = 2 - $2^{100}$ ) .

Step-by-step explanation :-

See the attachment.

Identity used :-

→ Dividend = Divisor × quotient + remainder .

→ p(x) = q(x) Q(x) + r(x) .

Therefore, the remainder

= ax + b.

= ( $2^{100}$ - 1) x + ( 2 - $2^{100}$ ) .

Hence, it is solved.

Answer 2

Answer :-

→a = ( 2^{100}- 1) and b = 2 - 2^{100}) .

Step-by-step explanation :-

Identity used :-

→ Dividend = Divisor × quotient + remainder .

→ p(x) = q(x) Q(x) + r(x) .

Therefore, the remainder

= ax + b.

= ( 2^{100} - 1) x + ( 2 - 2^{100} ) .