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10th Class Mathematics Quadratic Equations Question Bank Quadratic Equations

  • question_answer
    If 2 is a root of the equation \[{{x}^{2}}+bx+12=0\]and the equation \[{{x}^{2}}+bx+q=0\]has equal: roots, then q is equal to               

    A)  8                    

    B)         \[-8\]              

    C)  16                  

    D)         \[-16\]

    Correct Answer: C

    Solution :

    Since \[x=2\]is a root of the equation \[{{x}^{2}}+bx+12=0\] \[\Rightarrow \] \[{{(2)}^{2}}+b(2)+12=0\] \[\Rightarrow \]            \[2b=-16\] \[\Rightarrow \] \[b=-8\] Then, the equation \[{{x}^{2}}+bx+q\] becomes \[{{x}^{2}}-8x+q=0\]                      (ii) Since (1) has equal roots \[\Rightarrow \] \[{{b}^{2}}-4ac=0\] \[\Rightarrow \]  \[{{(-8)}^{2}}-4(1)q=0\]  \[\Rightarrow \] \[q=16\]


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