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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    Two roots of the cubic \[{{x}^{3}}+3{{x}^{2}}+kx-12=0\]are real and unequal but have the same absolute value. The value of k is

    A)  4                                

    B)   - 4

    C)  6                                

    D)  - 9

    Correct Answer: B

    Solution :

    Let the roots are r, -r and t Hence, \[r-r+t=-3\,\,\Rightarrow \,\,t=-3\] Now, product of the roots is \[(r)(-r)\,(t)\,=12\] \[-{{r}^{2}}(-3)\,=12\Rightarrow \,{{r}^{2}}=4\] Hence, roots are 2, - 2 and -3 Now, sum of the product taken two at a time is r \[(-r)+(-r)+tr=k\] \[\Rightarrow \,-4-6+6=k\Rightarrow \,-4\]


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