Równania i nierówności kwadratowe.
1.Rozwiąż równanie.
a)2xkwadrat + 3 = -7x
b)4xkwadrat + 12x + 9= 0
c)5xkwadrat - 6x + 6 = 0
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a)
2x² + 3 = -7x
2x² + 7x + 3 = 0
a = 2, b = 7 c = 3
Δ = b² - 4ac = 7² - 4 * 2 * 3 = 49 - 24 = 25
√Δ = 5
x1 = (-b - √Δ)/2a = (-7 - 5)/4 = -12/4 = -3
x1 = (-b + √Δ)/2a = (-7 + 5)/4 = -2/4 = -1/2
b)
4xkwadrat + 12x + 9= 0
4x² + 12x + 9= 0
a = 4, b = 12 c = 9
Δ = b² - 4ac = 12² - 4 * 4 * 9 = 144 - 144 = 0
x0 = -b/2a = -12/8 = -3/2 = -1,5
c)5xkwadrat - 6x + 6 = 0
5x² - 6x + 6 = 0
a = 5, b = -6 c = 6
Δ = b² - 4ac = (-6)² - 4 * 5 * 6 = 36 - 120 = -84 < 0
równanie nie posiada rozwiązania