Ta có : f(x) - g(x) = (3x² - x + 1) - (2x² - 3x - 7)

=> f(x) - g(x) = 3x² - x + 1 - 2x² + 3x + 7

=> f(x) - g(x) = x² + 2x + 1 + 7

=> f(x) - g(x) = (x + 1)² + 7

Mà ; (x + 1)² \(\ge0\forall x\)

Nên : f(x) - g(x) = (x + 1)² + 7 \(\ge7\forall x\)

Suy ra :  f(x) - g(x) = (x + 1)² + 7 \(>0\forall x\)

Vậy đa thức f(x) - g(x) vô nhiệm

Ta có f(x) + g(x) = 4x - 1. Khi đó nghiệm của đa thức tổng là x = 1/4. Chọn C

x=1/4 chon C

câu hỏi bạn ơi

a)

\(f\left(x\right)=x^4-5x^2-x^3+7x^2+3x-8=x^4-x^3+2x^2+3x-8\\ g\left(x\right)=x^3-3x^2-x^4-3x-17+2x^2=-x^4+x^3-x^2-3x-17\\ f\left(x\right)+g\left(x\right)=x^2-25\)

b) 

\(f\left(x\right)+g\left(x\right)=0\\ \Leftrightarrow x^2-25=0\Leftrightarrow x=\pm5\)

a) cho f(x )=0

\(=>2x^2-x=0=>x\left(2x-1\right)=0\)

\(=>\left[{}\begin{matrix}x=0\\2x=1\end{matrix}\right.=>\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\end{matrix}\right.\)

b)cho \(f\left(2\right)+g\left(2\right)=0\)

\(=>2.2^2-2+m.2^2+2m+1=0\)

\(8-2+4m+2m+1=0\)

\(6+2m\left(2+1\right)+1=0\)

\(6+6m=-1\)

\(6m=-7=>m=-\dfrac{7}{6}\)

Giúp mik vs 

a)\(f\left(x\right)=2x^2-x-3+5=\left(x+1\right)\left(2x-3\right)+5\)

Để \(f\left(x\right)⋮g\left(x\right)\Leftrightarrow\left(x+1\right)\left(2x-3\right)+5⋮\left(x+1\right)\)

\(\Leftrightarrow5⋮\left(x+1\right)\)

mà \(x+1\in Z\Rightarrow x+1\in U\left(5\right)=\left\{-1;1;5;-5\right\}\)

\(\Leftrightarrow x\in\left\{-2;0;4;-6\right\}\)

Vậy...

b) \(f\left(x\right)=3x^2-4x+6=\left(3x^2-4x+1\right)+5=\left(3x-1\right)\left(x-1\right)+5\)

Để \(f\left(x\right)⋮g\left(x\right)\Leftrightarrow\left(3x-1\right)\left(x-1\right)+5⋮\left(3x-1\right)\)

\(\Leftrightarrow5⋮\left(3x-1\right)\) mà \(3x-1\in Z\Rightarrow3x-1\in U\left(5\right)=\left\{-1;1;5;-5\right\}\)

\(\Leftrightarrow x\in\left\{0;\dfrac{2}{3};2;-\dfrac{4}{3}\right\}\) mà x nguyên\(\Rightarrow x\in\left\{0;2\right\}\)

Vậy...

c)\(f\left(x\right)=\left(-2x^3-7x^2-5x+2\right)+3\)\(=\left(-2x^3-4x^2-3x^2-6x+x+2\right)+3\)\(=\left[-2x^2\left(x+2\right)-3x\left(x+2\right)+\left(x+2\right)\right]+3\)

\(=\left(x+2\right)\left(-2x^2-3x+1\right)+3\)

Làm tương tự như trên \(\Rightarrow x+2\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)

\(\Leftrightarrow x\in\left\{-5;-3;-1;1\right\}\)

Vậy...

d)\(f\left(x\right)=x^3-3x^2-4x+3=x\left(x^2-3x-4\right)+3=x\left(x+1\right)\left(x-4\right)+3\)

Làm tương tự như trên \(\Rightarrow x+1\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)

\(\Rightarrow x\in\left\{-4;-2;0;2\right\}\)

Vậy...

Bài 1

Gợi ý bạn làm : Bạn thay \(x=-4;x=-3;x=0;x=1\) vào \(f\left(x\right);g\left(x\right)\)

\(\Rightarrow\) Nếu kết quả ra giống nhau thì là nghiệm , ra khác nhau thì không là nghiệm

VD : Thay \(x=-4\) vào \(f\left(x\right)\) và \(g\left(x\right)\)

\(f\left(-4\right)=4.\left(-4\right)^4-5\left(-4\right)^3+3.\left(-4\right)+2=1334\)

\(g\left(x\right)=-4.\left(-4\right)^4+5\left(-4\right)^3+7=-1337\)

Ra hai kết quả khác nhau 

\(\Rightarrow x=-4\) không là nghiệm

Bài 2

\(f\left(x\right)-g\left(x\right)=\left(-x^5+3x^2+4x+8\right)-\left(-x^5-3x^2+4x+2\right)\\ =-x^5+3x^2+4x+8+x^5+3x^2-4x-2\\ =\left(-x^5+x^5\right)+\left(3x^2+3x^2\right)+\left(4x-4x\right)+\left(8-2\right)\\ =6x^2+6\\ =x^2+1\\ =x^2+2.\dfrac{1}{2}x+\dfrac{1}{4}+\dfrac{3}{4}\\ =\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\forall x\)

\(\Rightarrow\) phương trình vô nghiệm 

\(\text{a)}f\left(x\right)-g\left(x\right)+h\left(x\right)=\left(x^3-2x^2+3x+1\right)-\left(x^3+x-1\right)+\left(2x^2-1\right)\)

                                    \(=x^3-2x^2+3x+1-x^3-x+1+2x^2-1\)

                               \(=\left(x^3-x^3\right)+\left(-2x^2+2x^2\right)+\left(3x-x\right)+\left(1+1-1\right)\)

                                  \(=2x+1\)

\(\text{b)Vì f(x)-g(x)+h(x)=0}\)

\(\Rightarrow2x+1=0\)

\(\Rightarrow2x\)        \(=0-1=-1\)

\(\Rightarrow\)   \(x\)        \(=\left(-1\right):2=\dfrac{-1}{2}\)

\(\text{Vậy x=}\dfrac{-1}{2}\text{ thì f(x)-g(x)+h(x)=0}\)

a: \(f\left(x\right)-g\left(x\right)+h\left(x\right)\)

\(=2x^3-2x^2+4x+2x^2-1=2x^3+4x-1\)

b: f(x)-g(x)+h(x)=0

\(\Leftrightarrow2x^3+4x-1=0\)

\(\Leftrightarrow x\simeq0,2428\)

a) f(x) - g(x) + h (x) = x³ - 2x² + 3x + 1 - (x³ + x - 1 ) + (2x² - 1 )

= x³ - 2x² + 3x + 1 - x³ - x + 1 + 2x² - 1

= (x³ - x³) + ( -2x² + 2x²) + (3x - x) + (1+1 - 1)

= 2x + 1

b) Đặt 2x + 1 = 0

=> 2x = -1

=> x = -1/2