Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

3x² - x - 4

Let,

⇒ 3x² - x - 4 = 0

⇒ 3x² - 4x + 3x - 4 = 0

⇒ x(3x - 4) + 1(3x - 4) = 0

⇒ (x + 1)(3x - 4) = 0

⇒ x + 1 = 0 or 3x - 4 = 0

⇒ x = -1 or 3x = 4

⇒ x = -1 or x = $\dfrac{4}{3}$.

Sum of zeroes = $-1 + \dfrac{4}{3} = \dfrac{-3 + 4}{3} = \dfrac{1}{3} = \dfrac{-(-1)}{3} = \dfrac{-\text{(Coefficient of x)}}{\text{(Coefficient of x}^2)}$

Product of zeroes = $-1 \times \dfrac{4}{3} = -\dfrac{4}{3} = \dfrac{\text{Constant term}}{\text{Coefficient of x}^2}$.

Hence, for zero of the polynomial 3x² - x - 4 = 0, x = -1, $\dfrac{4}{3}$.