| Assertion (A): The graph of the polynomial \[f(x)={{x}^{3}}-4x,\] cuts the X-axis at 3 different points. |
| Reason (R): The graph of a cubic polynomial always cross X-axis at least once and at most thrice. |
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] We have, \[f(x)={{x}^{3}}-4x=x({{x}^{2}}-4)\] |
| \[=x(x-2)\,\,(x+2)\] |
| \[\therefore \] \[x=0,\] 2, \[-2\] are three zeroes of \[f(x)\]. |
| \[\Rightarrow \] The curve \[y=f(x)\] cuts X-axis at three points. |
| \[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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