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Question

The value of '3a' for which one root of the quadratic equation
(a25a+3)x23(a1)x+2=0 is twice as large as other is

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Solution

Given equation
(a25a+3)x23(a1)x+2=0
For quadratic
a25a+30a5±132
Let the roots of the equation m,n
Now m=2n
So,
m+n=3(a1)a25a+3n=a1a25a+3(1)
and
2n2=2a25a+3n2=1a25a+3(2)
From (1) and (2)
(a1a25a+3)2=1a25a+3(a1)2=(a25a+3)a2+12a=a25a+33a=2

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