a) 7x² - x =0 x*(7x-1)=0 x=0 lub 7x-1=0 7x=1 /:7 x=1/7 b) 25x² - 4 = 0 25x²=4 /:25 x²= 4:25 x²=4/25 x=2/5 lub x=-2/5 c) -x² + 4x + 21 >0 a=-1, b=4, c=21 Δ=b²-4ac Δ=4²-4*(-1)*21 Δ=16 + 84 Δ=100 √Δ=10 x1=-b-√Δ/2a x1=-4-10/2*(-1) x1=-14/-2 x1=7 x2=-b+√Δ/2a x2=-4+10/-2 x2=6/-2 x2=-3 x∈(-3; 7) d) 2x² + 3x + 8> 0 a=2, b=3, c=8 Δ=3²-4*2*8 Δ=9-64 Δ=-55 nie ma pierwiastków e) 40x< -16x² -9 16x²+40x+9<0 a=16, b=40, c=9 Δ=40²-4*16*9 Δ=1600-576 Δ=1025 √Δ=32 x1=-40-32/2*16 x1=-72/32 x1=-2 8/32 x1=-2 1/4 x2=-40+32/2*16 x2=8/32 x2=1/4 x∈ (-2 1/4 ; 1/4)
a) 7x2 -x = 0 x(7x-1) =0 x=0,lub 7x-1= 0 7x = 1/7 x = 1/7 Odp.X1 =0, X2 =1/7 b) 25x2 -4 = 0 (5x+2)(5x-2) =0 5x+2 =0 5x =-2 /:5 x = -2/5 x = 2/5 Odp.X1 =-2/5, X2 =2/5 c) -x2+4x+21>0 delta = 16 +84 =100 Vd =10 X1 =(-4-10)/(-2) X1 =7 X2 = (-4+10)/(-2) X2 = -3 Odp. X> -3 d) 2x2 +3x + 8 > 0 delta =9 -64 delta<0, nie ma pierwiastków e) 40x <-16x2 -9 16x2 +40x +9 < 0 delta =1600 -576 =1024 Vd =32 X1 =(-40-32)/32 = -2 X2 =(-40+32)/32 = -1/4 = -0,25 Odp. X < -0,25
