1. The value of a, so that the sum of squares of the roots
of the equation x2 - (a - 2) x - a + 1 = 0 assume the
least value, is
[BITSAT 20141
(A) 2
(B) 0
(C) 3 (D) 1
Answers
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Let roots are α and β
from the equation α+β=a−2,αβ=−(a+1)
α2+β2=(α+β)2−2αβ
α2+β2=(a−2)2+2(a+1)=a2−2a+6
We have to find minimum value of a
a2−2a+6
⇒a2−2a+1+5
⇒(a−1)2+5
as least value of (a−1)2 is zero ⇒a−1=0
Therefore, for least value a=1
Hence, option 'B' is correct.
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