The function is,
\(y = 4{x^2} - 3x - 1\)
\(\begin{array}{l}0 = 4{x^2} - 3x - 1\\0 = 4{x^2} - 4x + x - 1\\0 = 4x\left( {x - 1} \right) + 1\left( {x - 1} \right)\\0 = \left( {4x + 1} \right)\left( {x - 1} \right)\end{array}\) \(\begin{array}{c}4x + 1 = 0\\x = - \frac{1}{4}\end{array}\)
\(\begin{array}{c}x - 1 = 0\\x = 1\end{array}\)
\(y = 4{x^2} - 3x - 1\)
Substitute y = 0 in the above function,
Use Zero Product Property to find the x-intercepts,
Or,
Hence, the x-intercepts are \(x = - \frac{1}{4}\) and\(x = 1\).