Đặt \(3x^2+x+4=0\)
\(\Leftrightarrow\left(x^2+x+4\right)+2x^2=0\)
\(\Leftrightarrow\left(x^2+2.\dfrac{1}{2}x+\dfrac{1}{4}\right)-\dfrac{1}{4}+4+2x^2=0\)
\(\Leftrightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{15}{4}+2x^2=0\)
Ta có:\(\left\{{}\begin{matrix}\left(x+\dfrac{1}{2}\right)^2\ge0\\2x^2\ge0\\\dfrac{15}{4}>0\end{matrix}\right.\)
\(\rightarrow\left(x+\dfrac{1}{2}\right)^2+\dfrac{15}{4}+2x^2\ge\dfrac{15}{4}>0\)
Vậy đa thức vô nghiệm
Đúng 3
Bình luận (0)
