Question

The value of a for which the sum of roots of the equation x^2-(a-2)x-a-1 assumes the least value

Answer 1

Q. The value of  for which the sum of the squares of the roots of the equation  assume the least value is:- A)2 B)3 C)0 D)1

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We are given the equation  and we are asked to find the value of a that minimizes the sum of the square of the roots:

We use the quadratic formula to find the roots with a=1,b=-(a-2), and c=-(a+1):

So 

This is minimized at a=1 (The graph of  is a parabola opening up; the minimum occurs at the vertex.)

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The minimum of the sum of the squares of the roots occurs when