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©The mean of the following frequencydistribution is 50, but the frequencies fi andf2 in classes 20-40 and 60-80, respectivelyare not known. Find these frequencies,if the sum of all the frequencies is 120.Class FrequencyR0-201720-40fi40-603260-80f 280-10019

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Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution INSTEAD of the usual two distinct solutions, then the two solutions MUST be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the VALUES of a are −1 and 9.


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