Question

CT các đa thức sau có 1 nghiệm chung

f(x) = 2x + 1

g(x) = x³ + \(\frac{1}{2}\) x² + 3x + \(\frac{3}{2}\)

Answer 1

\(f\left(x\right)=2x+1=0\)

\(\Leftrightarrow\)\(x=-\frac{1}{2}\)

\(g\left(x\right)=x^3+\frac{1}{2}x^2+3x+\frac{3}{2}=0\)

\(\Leftrightarrow\)\(x^2\left(x+\frac{1}{2}\right)+3\left(x+\frac{1}{2}\right)=0\)

\(\Leftrightarrow\)\(\left(x+\frac{1}{2}\right)\left(x^2+3\right)=0\)

\(\Leftrightarrow\)\(x+\frac{1}{2}=0\)  (vì x² + 3 > 0 )

\(\Leftrightarrow\)\(x=-\frac{1}{2}\)

Vậy nghiệm chung là:  \(x=-\frac{1}{2}\)