Đáp án:
$\begin{array}{l}
a)f\left( x \right) = 7{x^4} - 5{x^3} + 9{x^2} + 2x - \dfrac{1}{2}\\
f\left( 0 \right) = 7.0 - 5.0 + 9.0 + 2.0 - \dfrac{1}{2} = - \dfrac{1}{2}\\
g\left( x \right) = 7{x^4} - 5{x^3} + 8{x^2} + 2010x - \dfrac{1}{2}\\
\Leftrightarrow g\left( { - 1} \right) = 7.{\left( { - 1} \right)^4} - 5.{\left( { - 1} \right)^3} + 8.{\left( { - 1} \right)^2} + 2010.\left( { - 1} \right) - \dfrac{1}{2}\\
= 7 + 5 + 8 - 2010 - \dfrac{1}{2}\\
= \dfrac{{ - 3981}}{2}\\
b)h\left( x \right) = f\left( x \right) - g\left( x \right)\\
= 7{x^4} - 5{x^3} + 9{x^2} + 2x - \dfrac{1}{2}\\
- \left( {7{x^4} - 5{x^3} + 8{x^2} + 2010x - \dfrac{1}{2}} \right)\\
= {x^2} - 2008x\\
h\left( x \right) = 0\\
\Leftrightarrow {x^2} - 2008x = 0\\
\Leftrightarrow x.\left( {x - 2008} \right) = 0\\
\Leftrightarrow x = 0/x = 2008
\end{array}$
Vậy h(x) có nghiệm là 0 và 2008
