Verified answer

x² + 11x + 20 = 0

1) x₁ + x₂ = - 11

2) x₁ * x₂ = 20

3) (x₁ + x₂)² = (- 11)² = 121

4) x₁² + x₂² = (x₁ + x₂)² - 2x₁x₂ = (-11)² - 2 * 20 = 121 - 40 = 81

2) x² - 17x + c = 0

x₁ = - 7

(- 7)² - 17 * (- 7) + c = 0

49 + 119 + c = 0

c = - 168

x² - 17x - 168 = 0

D = (- 17)² - 4 * (- 168) = 289 + 672 = 961 = 31²