2.86
а)x²-3x+5≥0
D=9-20=-11<0 U a>0⇒x∈(-∞;∞)
б)x²+7x+10≤0
x1+x2=-7 U x1*x2=10⇒x1=-5 U x2=-2
x∈[-5;-2]
в)8x²-x+1≤0
D=1-32=-31<0 U a>0⇒нет решения
г)4x²-5x+6≥0
D=20-96=-71<0 U a>0⇒x∈(-∞;∞)
2.87
а)(x-1)(x-2)(x-3)≥0
x=1 x=2 x=3
_ + _ +
---------------[1]-----------[2]-----------------[3]---------------
x∈[1;2] U [3;∞)
б)(x-2)(x+2)(x-3)≤0
x=2 x=-2 x=3
_ + _ +
---------------[-2]-----------[2]-----------------[3]---------------
x∈(-∞;-2] U [2;3]
в)(x+1)(x+2)(x+3)≤0
x=-1 x=-2 x=-3
_ + _ +
---------------[-3]-----------[-2]-----------------[-1]---------------
x∈(-∞;-3] U [-2;-1]
г)(x-2)(x+2)(x+5)≥0
x=2 x=-2 x=-5
_ + _ +
---------------[-5]-----------[-2]-----------------[2]---------------
x∈[-5;-2] U [2;∞)
д)(x+1)²(x-1)≤0
x=-1 x=1
_ _ +
-----------------[-1]-------------------[1]-------------------
x∈(-∞;1]
е)(x-3)²(x-2)≥0
x=3 x=2
_ + +
------------------[2]----------------[3]---------------------
x∈[2;∞)