[administration]

Q. If one root of the equation (I-m)x²+Ix+1=0 is double of other and is real, find greatest value of m ?

[Wonder Boy]

Let the roots of quadratic equation be a and 2a .

so sum of roots = -I/(I-m) = 3a

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(1)

also product of roots = 1/(I-m) = 2a² —-(2)

—> -I(2a²) = 3a –>I= -3/2a

also I-m = 1/2a²

Since both roots are real. Hence D= B²– 4AC >=0

–> I² – 4(I-m)(1) >= 0

–> (-3/2a)² – 4 (1/2a²) >=0

9/4a² -2a² >=0

a² /4 >= 0 –> a²>=0

 

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