a) \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{5}{x}-{14}\)

\(\displaystyle{f{{\left({x}\right)}}}\Rightarrow{x}^{{2}}-{5}{x}-{14}={0}\)

\(\displaystyle{x}^{{2}}-{7}{x}+{2}{x}-{14}={0}\)

\(\displaystyle{x}{\left({x}-{7}\right)}+{2}{\left({x}-{7}\right)}={0}\)

\(\displaystyle{\left({x}+{2}\right)}{\left({x}-{7}\right)}={0}\)

Hence, the roots are \(x=-2,7\)

b) \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{64}\)

\(\displaystyle{f{{\left({x}\right)}}}={0}\Rightarrow{x}^{{2}}-{64}={0}\)

\(\displaystyle{\left({x}-{8}\right)}{\left({x}+{8}\right)}={0}\)

Hence, the roots are \(x=-8,8\)

c) \(\displaystyle{f{{\left({x}\right)}}}{6}{x}^{{2}}+{7}{x}-{3}\)

\(\displaystyle{f{{\left({x}\right)}}}={0}\Rightarrow{6}{x}^{{2}}+{7}{x}-{3}={0}\)

\(\displaystyle{6}{x}^{{2}}+{9}{x}-{2}{x}-{3}={0}\)

\(\displaystyle{3}{x}{\left({2}{x}+{3}\right)}-{1}{\left({2}{x}+{3}\right)}={0}\)

\(\displaystyle{\left({3}{x}-{1}\right)}{\left({2}{x}+{3}\right)}={0}\)

Hence, the roots are \(\displaystyle{x}=-\frac{{1}}{{3}},-\frac{{3}}{{2}}\)