Giải:
a) Để đa thức có nghiệm thì
\(x^2-4x=0\)
\(\Leftrightarrow\left(x-4\right)x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
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b) Để đa thức có nghiệm thì
\(\left(x-3\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)
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c) Để đa thức có nghiệm thì
\(\left(x-1\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x\in\varnothing\end{matrix}\right.\)
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Các ý còn lại làm tương tự.
a) \(\Leftrightarrow x\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
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f) \(\Leftrightarrow x^2+\dfrac{7}{2}x+\dfrac{5}{2}=0\)
\(\Leftrightarrow\left(x^2+\dfrac{7}{4}x\right)+\left(\dfrac{7}{4}x+\dfrac{7.7}{4.4}\right)+\dfrac{5}{2}-\dfrac{49}{16}=0\)
\(\Leftrightarrow x\left(x+\dfrac{7}{4}\right)+\dfrac{7}{4}\left(x+\dfrac{7}{4}\right)=\dfrac{49-5.8}{16}=\dfrac{9}{16}\)
\(\Leftrightarrow\left(x+\dfrac{7}{4}\right)^2=\left(\dfrac{3}{4}\right)^2\)
\(\left|x+\dfrac{7}{4}\right|=\dfrac{3}{4}\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{4}-\dfrac{3}{4}=\dfrac{-5}{2}\\x=-\dfrac{7}{4}+\dfrac{3}{4}=-1\end{matrix}\right.\)
d)
\(x^2+2x+1=0\)
\(\Leftrightarrow (x^2+x)+(x+1)=0\)
\(\Leftrightarrow x(x+1)+(x+1)=0\Leftrightarrow (x+1)^2=0\)
\(\Rightarrow x+1=0\leftrightarrow x=-1\)
e)
\(x^2+5x+4=0\)
\(\Leftrightarrow (x^2+x)+(4x+4)=0\)
\(\Leftrightarrow x(x+1)+4(x+1)=0\Leftrightarrow (x+1)(x+4)=0\)
\(\Rightarrow \left[\begin{matrix} x+1=0\\ x+4=0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=-1\\ x=-4\end{matrix}\right.\)