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

  • question_answer
    If the roots of \[{{x}^{2}}-bx+c=0\] are two consecutive integers, then \[{{b}^{2}}-4c\] is [RPET 1991; Kurukshetra CEE 1998; AIEEE 2005]

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: A

    Solution :

    Let the roots are \[\alpha \]and\[\alpha +1\], then, sum of roots\[=2\alpha +1=b\] product of roots \[=\alpha (\alpha +1)=c\] Now, \[{{b}^{2}}-4c={{(2\alpha +1)}^{2}}-4\alpha \,(\alpha +1)\] \[=4{{\alpha }^{2}}+1+4\alpha -4{{\alpha }^{2}}-4\alpha \] \[\therefore \ {{b}^{2}}-4c=1\].


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