Question

Cho 5a+3b+2c=0. CMR

pt \(ax^2+bx+c=0\)có nghiệm

Answer 1

\(5a+3b+2c=0\)

\(\Rightarrow3b=-5a-2c\) \(\Rightarrow b=\frac{-5a-2c}{3}\)

+ pt \(ax^{2\:}+bx+c\) = 0 có nghiệm

\(\Leftrightarrow b^2-4ac\ge0\)

\(\Leftrightarrow9\left[\left(\frac{-5a-2c}{3}\right)^2-4ac\right]\ge0\)

\(\Leftrightarrow\left(5a+2c\right)^2-36ac\ge0\)

\(\Leftrightarrow25a^2-16ac+4c^2\ge0\)

\(\Leftrightarrow\left(4a-2c\right)^2+9a^2\ge0\) ( luôn đúng )

Do đó ta có đpcm