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Question

If the roots of x3-12x2+12x-28=0 are in A.P, their common difference is


A

±3

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B

±2

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C

±1

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D

None of these

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Solution

The correct option is A

±3


Explanation for the correct option:

Find the value of a:

Let, a-d,a,a+d be the three roots of the given cubic equation x3-12x2+12x-28=0.

Where,

a is the first term and d is the common difference.

Now, find S1 and S3. Here S1 and S3 are the coefficient of cubic equation.

S1=-coefficientofx2coefficientofx3...1S1=a-d+a+a+d=3a

3a=--12a=123=4

Find the value of d:

S3=-constanttermcoefficientofx3...2S3=a-daa+d=a2-d2a=42-d24[a=4]=16-d24

416-d2=--28from216-d2=28416-d2=7d2=16-7d2=9d=9d=±3

Hence, the correct option is A.


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