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Question

Tìm No của đa thức :S(x)=2x^2-5x-3

Answer 1

\(S=2x^2-5x+3\)

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

\(=2\left(x^2-\dfrac{5}{4}x-\dfrac{5}{4}x+\dfrac{3}{2}\right)\)

\(=2\left[x\left(x-\dfrac{5}{4}\right)-\dfrac{5}{4}\left(x-\dfrac{5}{4}\right)-\dfrac{1}{16}\right]\)

\(=2\left[\left(x-\dfrac{5}{4}\right)^2-\dfrac{1}{16}\right]\)

\(=2\left(x-\dfrac{5}{4}\right)^2-\dfrac{1}{8}\)

Khi đó: \(2\left(x-\dfrac{5}{4}\right)^2=\dfrac{1}{8}\)

\(\Rightarrow\left(x-\dfrac{5}{4}\right)^2=\left(\dfrac{1}{4}\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{5}{4}=\dfrac{1}{4}\\x-\dfrac{5}{4}=-\dfrac{1}{4}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=1\end{matrix}\right.\)

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