2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Complex Numbers and Quadratic Equations

JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Relation between roots and coefficients

  • question_answer
    If the roots of \[a{{x}^{2}}+bx+c=0\] are \[\alpha ,\beta \] and the roots of \[A{{x}^{2}}+Bx+C=0\]are \[\alpha -k,\beta -k,\]then \[\frac{{{B}^{2}}-4AC}{{{b}^{2}}-4ac}\] is equal to [RPET  1999]

    A) 0

    B) 1

    C) \[{{\left( \frac{A}{a} \right)}^{2}}\]

    D)   \[{{\left( \frac{a}{A} \right)}^{2}}\]

    Correct Answer: B

    Solution :

    \[{{(\alpha -\beta )}^{2}}={{(\alpha +\beta )}^{2}}-4\alpha \beta =({{b}^{2}}-4ac)/{{a}^{2}}\]   ......(i) Also \[{{\left\{ (\alpha -k)-(\beta -k) \right\}}^{2}}\] = \[{{\{(\alpha -k)+(\beta -k)\}}^{2}}-4(\alpha -k)(\beta -k)\] =\[{{(-B/A)}^{2}}-4(C/A)\]\[=({{B}^{2}}-4AC)/{{A}^{2}}\] .....(ii) From (i) and (ii), \[({{b}^{2}}-4ac)/{{a}^{2}}=({{B}^{2}}-4AC)/{{A}^{2}}\] \ \[\frac{{{b}^{2}}-4AC}{{{b}^{2}}-4ac}={{\left( \frac{A}{a} \right)}^{2}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner