Question

In the question, a statement of assertion (𝐀) is followed by a statement of reason (𝐑). Mark the correct choice.

Assertion: The polynomial $p\left(x\right)=4x^3-3x^2+5x-6$ when divided by (𝒙 − 𝟏) gives zero as the remainder.

Remainder: (𝒙 − 𝟏) is a factor of the polynomial $p\left(x\right)=4x^3-3x^2+5x-6$.

• A. Assertion (A) is true, but reason (R) is false.
  
• B. Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
  
• C. Assertion (A) is false, but reason (R) is true.
  
• D. Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).
  

Answer 1

The correct option is B Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).


Solution:


Here we can see that the assertion is true explicitly.
Since the remainder of p(1) = 0, by factor theorem we can say that g(x) = (x - 1) is a factor of $p\left(x\right)=4x^3-3x^2+5x-6$. Thus the second statement is also true as it is the statement of the factor theorem.

Let's check whether reason (R) is the correct explanation or not for assertion (A).

Here we can clearly say that both assertion and reason statements are true and reason is also the correct explanation of assertion.