JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer The value of ?\[c\]?for which \[|{{\alpha }^{2}}-{{\beta }^{2}}|=\frac{7}{4}\], where \[\alpha \] and \[\beta \] are the roots of \[2{{x}^{2}}+7x+c=0\],  is

    A) 4

    B) 0

    C) 6

    D) 2

    Correct Answer: C

    Solution :

    We have \[\alpha +\beta =-\frac{7}{2}\]and \[\alpha \beta =\frac{c}{2}\] \ \[|{{\alpha }^{2}}-{{\beta }^{2}}|=\frac{7}{4}\,\,\Rightarrow {{\alpha }^{2}}-{{\beta }^{2}}=\pm \frac{7}{4}\] Þ \[(\alpha +\beta )(\alpha -\beta )=\pm \frac{7}{4}\] Þ \[-\frac{7}{2}\sqrt{\frac{49}{4}-2c}=\pm \frac{7}{4}\] Þ \[\sqrt{49-8c}=\mp 1\,\,\Rightarrow \,49-8c=1\,\Rightarrow c=6\]

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