Answer :
Answer:
k = - 2
Step-by-step explanation:
Given α and β are the zeros of x² - 6x + k = 0 , with
a = 1, b = - 6 and c = k , then
α + β = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{-6}{1}[/tex] = 6
αβ = [tex]\frac{c}{a}[/tex] = [tex]\frac{k}{1}[/tex] = k
Then solving
(α + β)² - 2αβ = 40
6² - 2k = 40
36 - 2k = 40 ( subtract 36 from both sides )
- 2k = 4 ( divide both sides by - 2 )
k = - 2