Question

If the sum of zeroes and product of zeroes are -8 and 6 then find the polynomial whose zeroes are alpha - beta and alpha + beta

Answer 1

let 2 roots b α and β
α+β= -8 , αβ = 6
α-β=√(α+β)² - 4αβ = √40 = 2√10
 let's new zeroes be a and b
a=α+β and  b = α-β
sum of roots of new one
a+b = -8+2√10
product would be ab = (α+β)(α-β) = (-8)(2√10) = -16√10
therefore  new equation x² - (-8+2√10)x -16√10 = 0

hope you'll get it