Given:

\(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{2}}−{3}{x}−{1}\)

To find roots

Put \(f(x)=0\)

\(\displaystyle{4}{x}^{{2}}-{3}{x}-{1}={0}\)

\(\displaystyle{4}{x}^{{2}}-{4}{x}+{x}-{1}={0}\)

\(\displaystyle{4}{x}{\left({x}-{1}\right)}+{1}{\left({x}-{1}\right)}={0}\)

\(\displaystyle{\left({4}{x}+{1}\right)}{\left({x}-{1}\right)}={0}\)

\(\displaystyle{x}={\frac{{-{1}}}{{{4}}}},{1}\)