If α ≠ β but, α 2 = 4 α - 2 and β 2 = 4 β - 2 , then the quadratic equation with roots α β and β α is

Question

If α ≠ β but, α 2 = 4 α - 2 and β 2 = 4 β - 2 , then the quadratic equation with roots α β and β α is, x 2 - 4 x + 2 = 0, x 2 - 6 x + 1 = 0, x 2 + 6 x - 1 = 0, x 2 + 4 x - 2 = 0

MARKS App · Accepted Answer

Since, α 2 = 4 α - 2 , β 2 = 4 β - 2 ⇒ α , β are the roots of x 2 = 4 x - 2 ⇒ α + β = 4 , α β = 2 The quadratic equation with roots α β , β α is, x 2 - α β + β α x + α β × β α = 0 ⇒ x 2 - ( α + β ) 2 - 2 α β α β x + 1 = 0 ⇒ x 2 - ( 16 - 4 ) 2 x + 1 = 0 ⇒ x 2 - 6 x + 1 = 0

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