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Mathematics

Assertion: If we subtract 15x2 - 9x + 1 from 1, then we get -15x2 + 9x.

Reason: The degree of 15x2 - 9x + 1 is 3 as it has three terms and degree of -15x2 + 9x is 2 as it has two terms.

  1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.

Algebraic Expressions

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Answer

Assertion (A) is true but Reason (R) is false.

Explanation

Assertion:

Subtracting 15x2 - 9x + 1 from 1:

1 - (15x2 - 9x + 1)

= 1 - 15x2 + 9x - 1 \quad[Simplifying brackets]

= (1 - 1) - 15x2 + 9x

= 0 - 15x2 + 9x

= - 15x2 + 9x

The result matches the statement exactly.

So, Assertion is true.

Reason is false because, the degree of a polynomial is determined by the highest power of the variable, not by the number of terms.

Degree of 15x2 - 9x + 1 = 2 (because the highest power of x is 2).

Degree of -15x2 + 9x = 2 (because the highest power of x is 2).

The Reason incorrectly claims the degree is 3 based on the number of terms.

Hence, option 3 is the correct option.

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