Question

Pomocy! obliczyć funkcje kwadratową

Answer 1

1.
3x² - 4x - 5 = 0
Δ = (- 4)² - 4 * 3 * (- 5) = 16 + 60 = 76
√Δ = √76 = 2√19
x₁ = (4 - 2√19)/6 = 2(2 - √19)/6 = (2 - √19)/3
x₂ = (4 + 2√19)/6 = 2(2 + √19)/6 = (2 + √19)/3
2
2x - 1 = 5x²
5x² - 2x + 1 = 0
Δ = (- 2)² - 4 * 5 * 1 = 4 - 20 = - 16
Δ < 0 to równanie nie ma pierwiastków , a rozwiązaniem jest zbiór pusty Q
3
(x - 4)(x + 2) = 5
(x - 4)(x + 2) - 5 = 0
x² - 4x + 2x - 8 - 5 = 0
x² - 2x - 13 = 0
Δ = (- 2) - 4 * 1 * (- 13) = 4 + 52 = 56
√Δ = √56 = 2√14
x₁ = (2 - 2√14)/2 = 2(1 - √14)/2 = 1 - √14
x₂ = (2 + 2√14)/2 = 2(1 + √14)/2 = 1 + √14
4
4(x - 4)² = 4
4(x² - 8x + 16) = 4
4x² - 32x + 64 - 4 = 0
4x² - 32x + 60 = 0 / : 4
x² - 8x + 15 = 0
Δ = (- 8)² - 4 * 1 * 15 = 64 - 60 = 4
√Δ = √4 = 2
x₁ = (8 - 2)/2 = 6/2 = 3
x₂ = (8 + 2)/ = 10/2 = 5