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

x² - 2x - 8

Let,

⇒ x² - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ x(x - 4) + 2(x - 4) = 0

⇒ (x + 2)(x - 4) = 0

⇒ x + 2 = 0 or x - 4 = 0

⇒ x = -2 or x = 4.

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

Product of zeroes = -2 × 4 = -8 = $\dfrac{-8}{1} = \dfrac{\text{Constant term}}{\text{Coefficient of x}^2}$

Hence, for zero of the polynomial x² - 2x - 8, x = -2, 4.