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if ` alpha , beta` be the roots of ` x^(2) -(a -2) x -a-1 =0` then the least value of ` alpha^(2) + beta^(2)` is (1) 0 (2) 1 (3) 3 (4) 5

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According to the question
`alpha + beta = a-2 and alpha beta = - (a+1)`
Now ` alpha^(2) +beta^(2) = (a-2)^(2) + 2a +2 =a^(2) -4a +4 + 2a +2 = (a -1)^(2) + 5 ge 5 `
` Rightarrow ` Least value of ` (alpha^(2) +beta^(2)) =5`
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