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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic inequations and Miscellaneous equations

  • question_answer
    If the sum of the two roots of the equation \[4{{x}^{3}}+16{{x}^{2}}-9x-36=0\] is zero, then the roots are  [MP PET 1986]

    A) 1, 2 -2

    B) \[-2,\frac{2}{3},-\frac{2}{3}\]

    C) \[-3,\frac{3}{2},-\frac{3}{2}\]

    D) \[-4,\frac{3}{2},-\frac{3}{2}\]

    Correct Answer: D

    Solution :

    Given equation\[4{{x}^{3}}+16{{x}^{2}}-9x-36=0\], Putting \[x=-4\]Þ \[-4\times 64+256+36-36=0\] Hence \[x=-4\] is a root of the equation Now reduced equation is \[4{{x}^{2}}(x+4)-9(x+4)=0\] Þ \[(x+4)(4{{x}^{2}}-9)=0\]Þ \[x=-4,x=\pm \frac{3}{2}\] Thus roots are \[-4\,,-\frac{3}{2},\frac{3}{2}\]


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