A real value of a , for which the sum of the roots of the equation x 2 - 2 a x + 2 a - 1 = 0 is equal to the sum of the square of its roots, is

Question

A real value of a , for which the sum of the roots of the equation x 2 - 2 a x + 2 a - 1 = 0 is equal to the sum of the square of its roots, is, 1 2, 3 2, 5 2, 2

MARKS App · Accepted Answer

Given, α + β = α 2 + β 2 Also, α + β = 2 a and α β = 2 a - 1 α + β = α + β 2 - 2 α β ⇒ 2 a = 2 a 2 - 2 2 a - 1 ⇒ 2 a = 4 a 2 - 4 a + 2 ⇒ 4 a 2 - 6 a + 2 = 0 ⇒ 2 a 2 - 3 a + 1 = 0 ⇒ a = 1 , 1 2

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