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

t² - 15

Let,

⇒ t² - 15 = 0

⇒ $(t - \sqrt{15})(t + \sqrt{15}) = 0$

⇒ $(t - \sqrt{15}) \text{ or } (t + \sqrt{15}) = 0$

⇒ $t = \sqrt{15} \text{ or } -\sqrt{15}$

Sum of zeroes = $\sqrt{15} + (-\sqrt{15}) = 0 = \dfrac{-\text{(Coefficient of t)}}{\text{(Coefficient of t}^2)}$

Product of zeroes = $-\sqrt{15} \times \sqrt{15} = -15 = \dfrac{\text{Constant term}}{\text{Coefficient of t}^2}$

Hence, for zero of the polynomial t² - 15, t = $-\sqrt{15}, \sqrt{15}$.