Question

Tìm nghiệm của đa thức C(x) = 2x² - 8x - 9 = 0

Answer 1

Ta có: \(C\left(x\right)=2x^2-8x-9=0\)

\(\Leftrightarrow2\left(x^2-4x-\frac{9}{2}\right)=0\)

\(\Leftrightarrow x^2-4x-\frac{9}{2}=0\)

\(\Leftrightarrow x^2-4x+4-\frac{17}{2}=0\)

\(\Leftrightarrow\left(x-2\right)^2=\frac{17}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=\sqrt{\frac{17}{2}}\\x-2=-\sqrt{\frac{17}{2}}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{4+\sqrt{34}}{2}\\x=\frac{4-\sqrt{34}}{2}\end{matrix}\right.\)

Vậy: \(S=\left\{\frac{4+\sqrt{34}}{2};\frac{4-\sqrt{34}}{2}\right\}\)