a) Ta có:
\(5{x^2} + 2x = 4 - x\)
\(\Leftrightarrow 5{x^2} + 2x - 4 + x=0\)
\(\Leftrightarrow 5{x^2} + 3x - 4 =0\)
\(\Leftrightarrow 5{x^2} + 3x +(- 4) =0\)
Suy ra \(a = 5,\ b = 3,\ c = - 4.\)
b) Ta có:
\(\dfrac{3 }{5}{x^2} + 2x - 7 = 3x + \dfrac{1}{2}\)
\( \Leftrightarrow \dfrac{3}{5}{x^2} +2 x -7-3x-\dfrac{1}{2}= 0\)
\( \Leftrightarrow \dfrac{3}{5}{x^2} -x -\dfrac{15}{2}= 0\)
\( \Leftrightarrow \dfrac{3}{5}{x^2} +(-1).x +{\left(-\dfrac{15}{2} \right)}= 0\)
Suy ra \(a = \dfrac{3 }{5},\ b = - 1,\ c = - \dfrac{15}{2}\).
c) Ta có:
\(2{x^2} + x - \sqrt 3 = \sqrt 3 x + 1\)
\( \Leftrightarrow 2{x^2} + x - \sqrt 3 - \sqrt 3 x -1 = 0\)
\( \Leftrightarrow 2{x^2} + (1-\sqrt 3)x + (-\sqrt 3 -1) = 0\)
Suy ra \(a = 2,\ b = 1 - \sqrt 3 ,\ c = - \sqrt 3 -1.\)
d) Ta có:
\(2{x^2} + {m^2} = 2(m - 1)x\)
\(\Leftrightarrow 2{x^2} +m^2-2(m-1)x=0 \)
\(\Leftrightarrow 2{x^2} -2(m-1)x+m^2=0 \)
\(\Leftrightarrow 2{x^2} + [-2(m-1)]x+m^2=0 \)
Suy ra \(a = 2,\ b = - 2(m - 1),\ c = {m^2}.\)
