Rozwiaz rownania i nierownosci kwadratowe:
a) -2x^{2}+3x-1=0
b) 5(x+1){2}=12x+4
c) 2x{2}+4x+4>0
d) x{2}-2x-3mniejsze lub rowne0
Prosze o szczegolowe rozwiazanie (rozpisanie rownan)
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a) -2 * x^2 + 3 * x - 1 = 0
delta = 3 * 3 - 4 * (-2) * (-1) = 9 - 8 = 1
sqrt(delta) = 1
x1 = (-3 -1) / (-4) = 1
x2 = (-3 +1) / (-4) = 1/2
b) 5 * (x+1)^2 = 12x + 4
5*x^2 + 10*x + 5 = 12x + 4
5*x^2 - 2x +1 = 0
delta = 4 - 4 * 5 = -16 => brak rozwiazania
c) 2 * x^2 +4x +4 > 0
delta = 16 - 4*4*2 = -16
z tego ze delta < 0 oraz a = 2 > 0 to x nalezy do R
d) x^2 - 2x - 3 <= 0
delta = 4 + 12 = 16
sqrt(delta) = 4
x1 =(2 - 4)/2 = -1
x2 = (2 + 4)/2 = 3
stad x^2 - 2x - 3 = (x - x1)(x-x2) = (x+1)(x-3) <= 0
jak narysujesz wykres to widac (bo a > 0), ze
x nalezy do <-1;3>