Question

Pomocy mam kartkówke
to jest funkcja kwadratowa

Answer 1

3(x - 2)² - 5x = 2
3(x² - 4x + 4) - 5x - 2 = 0
3x² - 12x + 12 - 5x - 2 = 0
3x² - 17x + 10 = 0
Δ = (- 17)² - 4 * 3 * 10 = 289 - 120 = 169
√Δ = √169 = 13
x₁ = (17 - 13)/6 = 4/6 = 2/3
x₂ = (17 + 13)/6 = 30/6 = 5

4(x - 2) - (x - 3)² = 0
4x - 8 - x² + 6x - 9 = 0
- x² + 10x - 17 = 0
Δ = 10² - 4 * - 1 * - 17 = 100 - 68 = 32
√Δ = √32 = 4√2
x₁ = (- 10 - 4√2)/- 2 = - 2(5 + 2√2)/- 2 = 5 + 2√2
x₂ = (- 10 + 4√2)/ - 2 = - 2(5 - 2√2)/ - 2 = 5 - 2√2

x⁶ - x³ - 2 = 0
za x³ wstawiamy z
z² - z - 2 = 0
Δ = (- 1)² - 4 * 1 * - 2 = 1 + 8 = 9
√Δ = √9 = 3
z₁ = (1 - 3)/2 = - 2/2 = - 1
z₂ = (1 + 3)/2 = 4/2 = 2
x³₁ = - 1
x₁ = ∛(- 1) = - 1
x³₂ = 2
x₂ = ∛2