Question

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

Assertion(A) : $x^3$ + $x$ has only one real zero.
Reason(R) : A polynomial of $n^{th}$ degree must have 𝒏 real zeros.

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

Answer 1

The correct option is D Assertion (A) is true, but reason (R) is false.


p(x) = $x^3$ + x = x($x^2$ + 1) = 0
x = 0 and $x^2$ = -1
It is clear from here that the given equation can have only one real zero.
So, assertion is true.
Now come to reason statement,
Reason statement is not true as it state that the a polynomial of $n^{th}$ degree must have 𝒏 real zeros but it is not true at all. Instead of this, a polynomial of $n^{th}$ degree have at most 𝒏 real zeros. Hence the Reason statement is false.

Assertion (A) is true, but reason (R) is false.