Question

assertion reasoning questions of chapter polynomials( NCERT class 9)​

Answer 1

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Answer 2

Question :-

Assertion (A) : The Remainder obtained when the polynomial x^(64)+x^(27)+1 is divided by x+1 is 1 .

Reason (R) : If f(x) is divided by x-a then the remainder is f(a) .

A) Both A & R are true and R is correct explanation of A .

B) Both A & R are true and R is not correct explanation of A .

C) A is true but R is false .

D) A is false but R is true .

Solution :-

We know that, according to remainder theorem when a polynomial p(x) is divided by (x - a) , remainder will be p(a) .

so, when polynomial f(x) = x^(64)+x^(27)+1 is divided by x+1 .

since,

→ x + 1 = 0

→ x = (-1)

then,

→ f(x) = x^(64)+x^(27)+1

→ f(-1) = (-1)⁶⁴ + (-1)²⁷ + 1

→ f(-1) = 1 - 1 + 1

→ f(-1) = 1

therefore, remainder will be 1 .

so,

Assertion (A) : The Remainder obtained when the polynomial x^(64)+x^(27)+1 is divided by x+1 is 1 .

• Correct .

Reason (R) : If f(x) is divided by x-a then the remainder is f(a) .

• Correct .

Hence, Option (A) Both A & R are true and R is correct explanation of A is correct answer .

Learn more :-

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. Find all the zeroes of the polynomial x4

– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

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