| Assertion (A): \[{{x}^{3}}+x\] has only one real zero. |
| Reason (R): A polynomial of nth degree must have n real zeroes. |
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: C
Solution :
| [c] Reason is false [a polynomial of nth degree has at most x zeroes.) |
| Again, \[{{x}^{3}}+x=x({{x}^{2}}+1)\] |
| which has only one real zero \[(x=0)\]\[[{{x}^{2}}+1\ne 0\,\,for\,\,all\,\,x\in R]\]assertion is true. |
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