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Comment upon the nature of roots …

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Comment upon the nature of roots of the following quadratic equation.    (x-2a)(x-2b)=4ab

 

    • Posted by Ayush Sharma 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Dharmendra Kumar 6 years, 9 months ago

    (x-2a)(x-2b)=4ab

    x(x-2b)-2a(x-2b)=4ab

    x2-2bx-2ax+4ab=4ab

    x2-(2b+2a)x+4ab-4ab=0

    x2-(2a+2b)x+0=0

    So on comparing with quadratic eqaution Ax2+Bx+C=0

    We get A=1 B=-(2a+2b)  C=0

    Discriminent D=B2-4AC

                              =(-(2a+2b))2-4×1×0

                              =(2a+2b)2-0

                              =(2a+2b)2 =(2(a+b))2=4(a+b)2

    Since square of any number cannot be negative, therefore D cannot be negative.

    So either D>0 or D=0

    Case1:- D=4(a+b)2>0 when a+b>0 , in this case roots are real and distinct.

    Case 2:- D=4(a+b)2=0 when a+b=0, in this case roots are real and repeated.

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