Question

If f(x) = x50 is divided by x2 − 3x + 2 then find the sum of coefficient of x and constant term in the remainder​

Answer 1

Given :- If f(x) = x^50 is divided by x² – 3x + 2. then find the sum of coefficient of x and constant term in the remainder.

Solution :-

given that, f(x) is divided by x² - 3x + 2 , which can be written as ,

→ x² - 3x + 2

→ x² - 2x - x + 2

→ x(x - 2) - 1(x - 2)

→ (x - 1)(x - 2)

now, according to remainder theorem , when a polynomial p(x) is divided by (x - a) , remainder will be f(a) .

so, when p(x) is divided by (x - 1) , we get,

→ p(x) = x^50

→ p(1) = (1)^50

→ p(1) = 1

and, when p(x) is divided by (x - 2) , we get,

→ p(x) = x^50

→ p(2) = (2)^50

then,

→ p(x) / (x - 1)(x - 2)

→ {p(x) / (x - 1)} * {p(x) / (x - 2)}

→ (1 * 2^50) remainder

→ 2^50 remainder .

therefore,

→ sum of coefficient of x in remainder = 0 .

and,

→ constant term in the remainder = 2^50 .

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