a) * Tính f(x)-g(x)
\(f\left(x\right)-g\left(x\right)=\left(2x-3\right)-\left(x+\dfrac{3}{4}\right)\)
\(f\left(x\right)-g\left(x\right)=2x-3-x-\dfrac{3}{4}\)
\(f\left(x\right)-g\left(x\right)=x-\dfrac{15}{4}\)
x.f(x)+3.g(x)
\(x.f\left(x\right)+3g\left(x\right)=x.\left(2x-3\right)+3.\left(x+\dfrac{3}{4}\right)\)
\(x.f\left(x\right)+3g\left(x\right)=2x^2-3x+3x+\dfrac{9}{4}\)
\(x.f\left(x\right)+3g\left(x\right)=2x^2+\dfrac{9}{4}\)
b) Tìm nghiệm của đa thức x.f(x)+3.g(x)
Ta có : \(2x^2+\dfrac{9}{4}=0\)
\(\Leftrightarrow2.\left(x^2+\dfrac{9}{8}\right)=0\)
\(\Leftrightarrow x^2+\dfrac{9}{8}=0\)
\(\Leftrightarrow x^2=\dfrac{-9}{8}\)
Ta có :\(x^2\ge0\)với mọi x
Mà : \(-\dfrac{9}{8}< 0\)
=> \(x^2=\dfrac{-9}{8}\) (vô lí)
=> Vô nghiệm.