Question

g(x) = \(5x^2-2x+5\)

f(x) = \(5x^2-6x-\dfrac{1}{3}\)

a) g(x) + F(x)

b) f(x) - g(x)

c) tìm nghiệm của f(x) - g(x)

Answer 1

Giải:

a) \(g(x)+f(x)=(5x^2-2x+5)+(5x^2-6x-\)\(\dfrac{1}{3}\)\()\)

\(=5x^2-2x+5+5x^2-6x-\dfrac{1}{3}\)

\(=\left(5x^2+5x^2\right)+\left(-2x-6x\right)+\left(5-\dfrac{1}{3}\right)\)

\(=10x^2-8x+\dfrac{14}{3}\)

b) \(f\left(x\right)-g\left(x\right)=\left(5x^2-6x-\dfrac{1}{3}\right)-\left(5x^2-2x+5\right)\)

\(=5x^2-6x-\dfrac{1}{3}-5x^2+2x-5\)

\(=\left(5x^2-5x^2\right)+\left(-6x+2x\right)+\left(-\dfrac{1}{3}-5\right)\)

\(=-4x-\dfrac{16}{3}\)

c) \(-4x-\dfrac{16}{3}=0\)

\(\Rightarrow-4x=\dfrac{16}{3}\)

\(\Rightarrow x=\dfrac{16}{3}:\left(-4\right)\)

\(\Rightarrow x=\dfrac{-4}{3}\)

Vậy nghiệm của đa thức là \(\dfrac{-4}{3}\).