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10th Class Mathematics Quadratic Equations Question Bank Quadratic Equations

  • question_answer
    If one root of the equation \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\] is 1, then the other root is __.                             

    A)  \[\frac{b(c-a)}{a(b-c)}\]       

    B)  \[\frac{a(b-c)}{c(a-b)}\]        

    C)         \[\frac{a(b-c)}{b(c-a)}\]       

    D)         \[\frac{c(a-b)}{a(b-c)}\]                    

    Correct Answer: D

    Solution :

    Given equation is \[a(b-c){{x}^{2}}+b(c-a)x+c(a-b)=0\] Let \[\alpha \]  be the other root. then Product of roots \[=\alpha \times 1=\frac{c(a-b)}{a(b-c)}\] \[\Rightarrow \]   \[\alpha =\frac{c}{a}\,\left( \frac{a-b}{b-c} \right)\]


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