Question

if alpha and beta are zeroes of the polynomial x^2+8x+6 Then find a polynomial with zeroes (Alpha -beta) , (alpha + beta)

Answer 1

α + β = -8
αβ = 6
(α- β)² =  (-8)² - 4 * 6 = 40

α - β = + - 2√10


Polynomial with zeroes as α-β and α+β :

x² - (α - β+ α + β ) x + (α - β)(α + β)

x² - (2√10 - 8 ) x + (-8 )(2√10)  =  x² + 2 (4 - √10) x - 16√10

OR
x² - (-2√10 - 8) + (-8) (-2√10)  = x² + 2(4+√10) + 16√10