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10th Class Mathematics Quadratic Equations Question Bank Quadratic Equation

  • question_answer
    If \[a-b,b-c\] are the roots of \[a{{x}^{2}}+bx+c=0\], then find the value of \[\frac{(a-b)(b-c)}{2(c-a)}\].

    A)  \[\frac{b}{c}\]                          

    B)  \[\frac{c}{2b}\]

    C)  \[\frac{ab}{c}\]                        

    D)  \[\frac{bc}{a}\]

    Correct Answer: B

    Solution :

    (b): \[(a-b)(b-c)=\]product of the roots \[=\frac{c}{a}\] Also \[(c-a)=-\left[ (a-b)+(b-c) \right]\] = ? sum of roots = \[\frac{b}{a}\] \[\Rightarrow \frac{(a-b)(b-c)}{2(c-a)}=\frac{\frac{c}{a}}{\frac{2b}{a}}=\frac{c}{2b}\]


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