My First Quadratic
Algebra
Level
3
The value of for which the sum of the squares of the roots of the equation assumes the least value is?
The answer is 1.
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1 solution
let the roots be α , β , by vieta's, α 2 + β 2 = ( a − 2 ) 2 − 2 ( − a − 1 ) a 2 − 2 a + 6 = ( a − 1 ) 2 + 5 it will obtain its minima at 1 for ( a − 1 ) 2 = 0 . hence the answer is 1.