-4k²-16x+9=0 a = -4 b = -16 c = 9 Δ = b² -4ac Δ = (-16)² -4*(-4) *9 = 256 + 144 = 400 √Δ = √400 = 20 k₁ = (-b-√Δ): (2*a) k₁ = [-(-16) - 20] :2*(-4) = (16 -20): (-8) = (-4) :(-8) = 0,5 k₂= (-b+√Δ): (2*a) k₂ = [-(-16) +20] :2*(-4) = (16 +20): (-8) = ( 36) :(-8) = - 4,5 2(2x-3)(x+1)-5(x-1)²= 2(x-2)(x-1) 2(2x² +2x -3x -3) -5(x² -2x +1) = 2(x² -x -2x + 2) 4x² -2x -6 -5x² +10x -5 = 2x² -6x +4 -x² + 8x - 11 = 2x² -6x +4 -x² -2x² +8x +6x -11-4 = 0 -3x² +14x -15 = 0 a = -3 b = 14 c = -15 Δ = b² -4ac Δ = 14² -4*(-3)*(-15) = 196 -180 = 16 √Δ = √16 = 4 x₁ = (-b-√Δ): (2*a) x₁ = (-14-4):[2*(-3)] = (-18): (-6) = 3 x₂= (-b+√Δ): (2*a) x₂ = (-14+4):[2*(-3)] = (-10): (-6)= 5/3 -x²-3x+4≥0 a= -1 b = -3 c = 4 Δ = 9 +16 =25 √Δ = 5 x₁ = (-2):(-2) = 1 x₂ = 8:(-2) = -4 Parabola skierowana est ramionami w dół x ∈ < -5, 1> x²-7x+12>0 a = 1 b = -7 c = 12 Δ = (-7)² -4*1*12= 49 -48 = 1 √Δ = 1 x₁ = 6 : 2 = 3 x₂ = 8 : 2 = 4 Ramiona paraboli skierowane są do góry x ∈ (-∞, 3) ∨( 4 +∞) -4a²-16a+9<0 a = -4 b = -16 c = 9 Δ = (-16)² -4*(-4)*(-16) = 256 -256 = 0 √Δ = 0 a₁ = 16 : (-8) = -2 a₂ = 16 : (-8) = -2 podwójny pierwiastek Ramiona paraboli skierowane są w dół a ∈ R - { -2} x²-6x+9≤0 a = 1 b = -6 c = 9 Δ = (-6)² -4*1*9= 36 -36 = 0 √Δ = 0 x₁ = x₂ = (-b): 2a x₁ = x₂ = 6 : 2*1 = 6 : 2 = 3 Ramiona paraboli skierowane są w górę x = 3
