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10th Class Mathematics Polynomials Question Bank Polynomial

  • question_answer
    If a and b can take values 1, 2, 3, 4, then the number of the equations of the form \[a{{x}^{2}}+bx+1=0\] having real roots is

    A)  10                               

    B)  7        

    C)  6                                

    D)  12

    Correct Answer: B

    Solution :

    (b): For real roots, \[{{b}^{2}}-4ac\ge 0\] \[\Rightarrow {{b}^{2}}-4ac\ge 0\Rightarrow {{b}^{2}}\ge 4a\] For a = 1; can take values 2, 3, 4 \[\therefore \]Admissible pairs are (1, 2) (1, 3) (1, 4) Similarly other ADMISSIBLE PAIRS are: (2, 3), (2, 4), (3, 4), (4, 4) Hence total seven pairs \[\Rightarrow \] seven eqns.   


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