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10th Class Mathematics Quadratic Equations Question Bank Quadratic Equations

  • question_answer
    The roots of the equation \[{{x}^{2/3}}+{{x}^{1/3}}-2=0\]are _____.

    A)  \[1,-8\]  

    B)                     \[1,-2\]           

    C)                     \[\frac{2}{3},\frac{1}{3}\]               

    D)                     \[-2,-8\]                      

    Correct Answer: A

    Solution :

                        Given equation is \[{{x}^{2/3}}+{{x}^{1/3}}-2=0\]          Let   \[y={{x}^{1/3}}\] \[\Rightarrow \] \[{{y}^{2}}+y-2=0\] \[\Rightarrow \]\[{{y}^{2}}+2y-y-2=0\] \[\Rightarrow \]\[(y-1)(y+2)=0\] \[\Rightarrow \]\[y=1\] or \[y=-2\]\[\Rightarrow \] \[{{x}^{1/3}}=1\]or \[{{x}^{1/3}}=-2\] \[\Rightarrow \] \[x=1\]  or  \[x=-8\]


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