JEE Main & Advanced JEE Main Paper (Held on 09-4-2019 Morning)

  • question_answer If \[\left( x \right)\]is a non-zero polynomial of degree four, having local extreme points at \[x=1,0,1;\]then the set \[S=\]\[\{x\in R:\left( x \right)=\left( 0 \right)\}\] Contains exactly :             [JEE Main 9-4-2019 Morning]

    A) four irrational numbers.

    B) two irrational and one rational number.

    C)  four rational numbers.

    D) two irrational and two rational numbers.

    Correct Answer: B

    Solution :

    \[f'(x)=\lambda (x+1)(x-0)(x-1)=\lambda ({{x}^{3}}-x)\]           \[\Rightarrow \]\[f(x)=\lambda \left( \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right)+\mu \]           Now\[f(x)=f(0)\]           \[\Rightarrow \lambda \left( \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right)+\mu =\mu \]\[\Rightarrow x=0,0,\pm \sqrt{2}\]             Two irrational and one rational number

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