Câu 1:
a.P(x)=2x³-2x+x²-x³+3x+2
=[2x³+(-x³)]+x²+(-2x+3x)+2
=x³+x²+x+2
Q(x)=3x³-4x²+3x-4x-4x³+5x²+1
=(3x³-4x³)+(-4x²+5x²)+[3x+(-4x)]+1
=-x³+x²-x+1
b.M(x)=P(x)+Q(x)=(x³+x²+x+2)+(-x³+x²-x+1)
=x³+x²+x+2-x³+x²-x+1
=(x³-x³)+(x²+x²)+(x-x)+(2+1)
=2x²+3
N(x)=P(x)-Q(x)=(x³+x²+x+2)-(-x³+x²-x+1)
=x³+x²+x+2+x³-x²+x-1
=(x³+x³)+(x²-x²)+(x+x)+(2-1)
=2x³+2x+1
c. Vì x²≥0 với mọi x∈R
nên 2x²≥0 với mọi x∈R
⇒2x²+3>0 với mội x∈R
⇒M(x)>0
Vậy M(x) không có nghiệm
Câu 4:
P($\frac{1}{2}$)=a.1/2² +5.1/2-3
P(x)=a.1/4+5/2-3=0
a.1/4+(-1/2)=0
a.1/4 =0-(-1/2)
a.1/4 =1/2
a =1/2:1/4
a =2
câu 5:
a)A(x)=5x³+4x-6x²-7=5x³-6x²+4x-7
B(x)=-5x³-2x+12+5x²=-5x³+5x²-2x+12
b)C(x)=A(x)+B(x)=(5x³-6x²+4x-7)+(-5x³+5x²-2x+12)
=5x³-6x²+4x-7-5x³+5x²-2x+12
=(5x³-5x³)+(-6x²+5x²)+(4x-2x)+(-7+12)
=-x²+2x+5
A(x)-B(x)=(5x³-6x²+4x-7)-(-5x³+5x²-2x+12)
=5x³-6x²+4x-7+5x³-5x²+2x-12
=(5x³+5x³)+[-6x²+(-5x²)]+(4x+2x)+[-7+(-12)]
=10x³-11x²+6x-19
