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Question

The value of a, so that the sum of squares of the root of the equations x2-(a-2)x-a+1=0 assume the least value, is


A

2

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B

0

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C

3

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D

1

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Solution

The correct option is D

1


Explanation for the correct option:

Find the value of a:,

An equation x2-(a-2)x-a+1=0 is given.

Assume that, α and β are the roots of the given equation.

Therefore, the sum of squares of the roots is α2+β2.

α2+β2=(α+β)2-2α·β...(1)

We know that the sum of roots can be given by -ba.

Therefore, α+β=a-2...(2).

We know that the product of roots can be given by ca.

Therefore, α·β=1-a...(3).

From equation (1),(2) and (3), we get

α2+β2=(a-2)2-2(1-a)α2+β2=a2+4-4a-2+2aα2+β2=a2-2a+2α2+β2=a2-2a+1+1α2+β2=a-12+1

Since, the least possible value of the sum of squares of the root of the given equation is only when a-1=0.

Therefore, the value of a=1.

Hence, option (D) is the correct option.


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