Question

prove that the roots of x^2+(1-k)x+k-3=0 are real for all real values of k​

Answer 1

Explicação passo-a-passo:

Δ ≥ 0

(1-k)² - 4 . 1 . (k-3) ≥ 0

1 -2k + k² - 4k + 12 ≥ 0

k² - 6k + 13 ≥ 0

k = (6 ± 4i)/2

k = 3 ± 2i