a) f(x)=x²-9x+8
f(x) = 0
x²-9x+8=0
Δ=(-9)²-4·1·8=81-32=49 , √Δ=√49=7
x1=(9-7)/2
x1=1
x2=(9+7)/2
x2=8
f(x) > 0
x∈(-∞,1)∪(8,∞)
f(x) < 0
x∈(1,8)
b) f(x)=2x²-5x-12
2x²-5x-12=0
Δ=(-5)²-4·2·(-12)=25+96=121, √Δ=√121=11
x1=(5-11)/4
x1=-3/2
x2=(5+11)/4
x2=4
f(x) > 0 dla x∈(-∞,-3/2)∪(4,∞)
f(x) < 0 dla x∈(-3/2,4)
c) f(x)=-2x²-x+21
-2x²-x+21=0|:(-1)
2x²+x-21=0
Δ=1²-4·2·(-21)=1+168=169 , √Δ=√169=13
x1=(-1-13)/4
x1=-7/2
x2=(-1+13)/4
x2=3
f(x) > 0 dla x∈(-7/2,3)
f(x) < 0 dla x∈(-∞,-3/2)∪(3,∞)
d) f(x)=3x²+10x+3
3x²+10x+3=0
Δ=10²-4·3·3=100-36=64, √Δ=√64=8
x1=(-10-8)/6
x1=-3
x2=(-10+8)/6
x2=-1/3
f(x) > 0 dla x∈(-∞,-3)∪(-1/3,∞)
f(x) < 0 dla x∈(-3,-1/3)
e) f(x)=-6x²+13x-6
-6x²+13x-6=0|:(-1)
6x²-13x+6=0
Δ=(-13)²-4·6·(-6)=169+144=313,√Δ=√313
x1=(13-√313)/12
x2=(13+√313)/12
f(x) > 0 dla x∈((13-√313)/12,(13+√313)/12)
f(x) < 0 dla x∈(-∞,(13-√313)/12)∪((13+√313)/12, ∞)
f) f(x)=2(x-1/2)²-9/2
2(x-1/2)²-9/2=0|:2
(x-1/2)²-9/4=0
[(x-1/2)+3/2][(x-1/2)-3/2]=0
(x-1/2+3/2)(x-2)=0
(x+1)(x-2)=0
x+1=0 ∨ x-2=0
x=-1 ∨ x=2
x∈(-∞,-1)∪(2,∞)
f(x) < 0 dla x∈(-1,2)
