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KVPY Sample Paper KVPY Stream-SX Model Paper-30

  • question_answer
    The ratio of the roots of the equation \[a{{x}^{2}}+bx+c=0\] is same as the ratio of the roots of the equation \[A{{x}^{2}}+Bx+C=0\]. If \[{{D}_{1}}\] and \[{{D}_{2}}\] are the discriminants of \[a{{x}^{2}}+bx+c=0\] and \[A{{x}^{2}}+Bx+C=0\] respectively, then \[{{D}_{1}}:{{D}_{2}}=\]

    A) \[\frac{{{a}^{2}}}{{{A}^{2}}}\]

    B) \[\frac{{{b}^{2}}}{{{B}^{2}}}\]

    C) \[\frac{{{c}^{2}}}{{{C}^{2}}}\]       

    D) None of these

    Correct Answer: B

    Solution :

    \[\frac{\alpha }{\beta }=\frac{\gamma }{\delta }.\]Apply C and D ; \[\frac{\alpha +\beta }{\alpha -\beta }=\frac{\gamma +\delta }{\gamma -\delta }\]Square both sides
    \[\therefore \frac{{{b}^{2}}}{{{b}^{2}}-4ac}=\frac{{{B}^{2}}}{{{B}^{2}}-4AC}\]  \[\therefore \frac{{{D}_{1}}}{{{D}_{2}}}=\frac{{{b}^{2}}}{{{B}^{2}}}\Rightarrow (b)\]


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