The value of α for which the sum of...
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The value of α for which the sum of the squares of the roots of the equation  

x^2 – ( α– 2)x – a-1 = 0  

assume the least value is  

(A) 1  

(B) 0  

(C) 3  

(D) 2

JEE/Engineering Exams
Maths
Solution
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The value of α for which the sum of the squares of the roots of the equation    x^2 – ( α– 2)x – a-1 = 0    assume the least value is
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Given:- x2-a-2x-a-1=0 Find:- a for whole α2+β2 is minimum Let the roots are α and β     α+β=-BA=a-2      αβ=CA=-a+2  α2+β2=α+β2-2αβ              =a-22+2(a+2)               =a2+4-4a+2a+2               =a2-2a+6               =a2-2a+1+5               =(a-1)2+5 α2+β2 is minimum when a=1 a=1 (A) 

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