The minimum value of the sum of the squares of the roots of x 2 + 3 - a x = 2 a - 1 is

Step-by-step solution

Let α , β be the roots of the equation x 2 + 3 - a x + 1 - 2 a = 0 Then, sum of roots α + β = a - 3 And product of roots α β = 1 - 2 a We know that α 2 + β 2 = α + β 2 - 2 α β ∴ α 2 + β 2 = a - 3 2 - 2 1 - 2 a = a 2 - 2 a + 7 = a - 1 2 + 6 ∴ Minimum value of α 2 + β 2 = 6 at a = 1 .