a. 4² + 1 = 0
x(4x + 1) = 0
x = 0 lub 4x + 1 = 0
4x = -1 /:4
x = -1/4
x1 = 0, x2 = -1/4
b. x² - 6x + 9 = 0
a = 1 b = 6 c = 9
Δ = b² - 4ac
Δ = 6² - 4 * 1 * 9
Δ = 36 - 36
Δ = 0 jedno miejsce zerowe
x = -b/2a
x = -6/2 * 1
x = -3
c. -5x² + x = 0
a = -5 b = 1 c = 0
Δ = b² - 4ac
Δ = 1² - 4 * (-5) * 0
Δ = 1 - 0
Δ = 1 czyli Δ > 0 to dwa rozwiązania
Pierwiastek z Δ = 1
x1 = -b - pierwiastek Δ / 2a
x1 = -1 - 1 / 2 * (-5)
x1 = -2 / -10
x1 = 1/5
x2 = -b + pierwiastek z Δ / 2 * a
x2 = -1 + 1 / 2 * (-5)
x2 = 0 / -10
x2 = 0
x1 = 1/5, x2 = 0
d. -2(x - 3)(x + 4) = 0
-2x² - 2x + 24 = 0
a = -2 b = 2 c = 24
Δ = b² - 4ac
Δ = 2² - 4 * (-2) * 24
Δ = 4 + 192
Δ = 196 czyli Δ > 0 to dwa rozwiązania
Pierwiastek z Δ = 14
x1 = -b - pierwiastek Δ / 2a
x1 = -2 - 14 / 2 * (-2)
x1 = -16 / -4
x1 = 4
x2 = -b + pierwiastek z Δ / 2 * a
x2 = -2 + 14 / 2 * (-2)
x2 = 12 / -4
x2 = -3
x1 = 4, x2 = -3
e. 14 + 5x - x² = 0
a = -1 b = 5 c = 14
Δ = b² - 4ac
Δ = 5² - 4 * (-1) * 14
Δ = 25 + 56
Δ = 81 czyli Δ > 0 to dwa rozwiązania
Pierwiastek z Δ = 9
x1 = -b - pierwiastek Δ / 2a
x1 = -5 - 9 / 2 * (-1)
x1 = -14 / -2
x1 = 7
x2 = -b + pierwiastek z Δ / 2 * a
x2 = -5 + 9 / 2 * ( -1)
x2 = 4 / -2
x2 = -2
x1 = 7, x2 = -2
Δ = delta
