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10th Class Mathematics Polynomials Question Bank Polynomial

  • question_answer
    Find the zeroes of the polynomials \[f(y)={{y}^{3}}+{{y}^{2}}-9y-9\], if two zeroes are equal in magnitude but opposite in sign. \[\alpha ,-\alpha ,\beta \]

    A)  \[(1,-1,-3)\]                   

    B)  \[(+3,-3,-1)\]

    C)  \[(-2+\sqrt{3},2-\sqrt{3},-1)\]     

    D)  \[\left( \frac{1}{2},\frac{1}{2},9 \right)\]

    Correct Answer: B

    Solution :

    (b): Let zeros be \[\alpha ,-\alpha ,\beta \] Then, Sum of roots\[=\beta =-1\]: Also, \[\alpha \beta -\alpha \beta -{{\alpha }^{2}}=-9\Rightarrow \alpha =\pm 3\] \[\therefore \] Roots are \[=\left( 3,-3,-1 \right)\] or \[\left( -3,\text{ }3,-1 \right)\].


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