Roots of the equation #px(2-x)=x-4m# are #a/3# an #b/3# and while #a+b=9#, #ab=12#. Find #p# and #m#?

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Answer 1 · 2017-02-21T09:48:29

#p=-1# and #m=1/3#

In a quadratic equation #ax^2+bx+c=0#,

we have sum of roots as #-b/a# and product of roots as #c/a#

Hence, as #px(2-x)=x-4m#

we have #-px^2+2px-x+4m=0#

or #px^2-(2p-1)x-4m=0#

and as its roots are #a/3# and #b/3#, we have

#a/3+b/3=(2p-1)/p# or #(2p-1)/p=(a+b)/3=9/3=3#

Hence #2p-1=3p# or #p=-1#

Further #a/3xxb/3=(-4m)/p=4m# (as #p=-1#)

Hence #4m=(ab)/9=12/9=4/3# i.e. #m=1/3#