PRZEDSTAW W POSTACI ILOCZYNOWEJ(JEŚLI ISTNIEJE) NASTEPUJACE FUNKCJE KWADRATOWE!
a) y=7x²-9x+2
Δ = 81-56 = 25, √Δ = 5
x₁ = (-9 - 5)/14 = -1
x₂ = (-9 + 5)/14 = -2/7
y=7x²-9x+2 = (x + 1)(x + 2/7)
b) y=x²+x-30
Δ = 1 + 120 = 121, √Δ = 11
x₁ = (-1 - 11)/2 = -6
x₂ = (-1 + 11)/2 = 5
y=x²+x-30 = (x + 6)(x - 5)
c) y=-4x²+17x = -4x(x - 17/4)
Rozwiąż równanie kwadratowe!
a) x²-16=0
(x + 4)(x - 4) = 0
ODP: x = 4 v x = -4
b) 6x²+x-1=0
Δ = 1 + 24 = 25, √Δ = 5
x₁ = (-1 - 5)/12 = -1/2
x₂ = (-1 + 5)/12 = 1/3
ODP: x = -1/2 v x = 1/3
c) 5x²+9x-14=0
Δ = 81 + 280 = 361, √Δ = 19
x₁ = (-9 - 19)/10 = -2,8
x₂ = (-9 + 19)/10 = 1
ODP: x = -2,8 v x = 1
a)x²-9=0
(x + 3)(x - 3) = 0
ODP: x = -3 v x = 3
b)-2x²+6x=0
-2x(x - 3) = 0
ODP: x = 0 v x = 3
c)x²-8x+15=0
Δ = 64 - 60 = 4, √Δ = 2
x₁ = (8 - 2)/2 = 3
x₂ = (8 + 2)/2 = 5
ODP: x = 3 v x = 5
d)3x²+10x+3=0
Δ = 100 - 36 = 64, √Δ = 8
x₁ = (-10 - 8)/6 = -3
x₂ = (-10 + 8)/6 = -1/3
ODP: x = -3 v x = -1/3
