By splitting the middle term

4x² - 3x - 1 = 0

4x² - (4x - x) - 1 = 0

4x² - 4x + x - 1 = 0

4x(x - 1) + (x - 1) = 0

(x - 1)(4x - 1) = 0

⇒ x = 1, - 1/4

Verification:

Sum of the zeroes = - (coefficient of x) ÷ coefficient of x²

α + β = - b/a

1 - 1/4 = - (- 3)/4

= 3/4 = 3/4

Product of the zeroes = constant term ÷ coefficient of x²

α β = c/a

1(- 1/4) = - 1/4

- 1/4 = - 1/4