| Assertion (A): The polynomial \[p(x)={{x}^{3}}+x\] has one real zero. |
| Reason (R): A polynomial of nth degree has at most n 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: A
Solution :
| [a] Reason is clearly true. |
| We have, \[p(x)={{x}^{3}}+x\] |
| \[p(x)=0\Rightarrow {{x}^{3}}+x=0\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,x({{x}^{2}}+1)=0\Rightarrow x=0\] or \[{{x}^{2}}+1=0\] |
| But, \[{{x}^{2}}+1\ne 0\] for any real value of x |
| \[[{{x}^{2}}+1>0]\] |
| \[\therefore \,\,\,p(x)\] has one real zero, namely 0. |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
You need to login to perform this action.
You will be redirected in
3 sec
