11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer The value of 'a' for which the equations \[{{x}^{2}}-3x+a=0\] and \[{{x}^{2}}+ax-3=0\] have a common root is  [Pb. CET 1999]

    A) 3

    B) 1

    C) - 2

    D) 2

    Correct Answer: D

    Solution :

    Given equations are \[{{x}^{2}}-3x+a=0\]    ??(i) and             \[{{x}^{2}}+ax-3=0\]                  ??(ii) Subtracting (ii) from (i), we get Þ  \[-3x-ax+a+3=0\] \[\Rightarrow (a+3)(-x+1)=0\] Þ  either \[a=-3\] or \[x=1\] When \[a=-3,\]the two equations are identical. So, we take \[x=1,\] which is the common root of the two equations. Substituting \[x=1\] in (i), we get  \[1+a-3=0\Rightarrow a=2.\]

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