Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) \(x^2 - 2x - 8\)
(ii) \(4s^2 - 4s + 1\)
(iii) \(6x^2 - 3 - 7x\)
(iv) \(4u^2 + 8u\)
(v) \(t^2 - 15\)
(vi) \(3x^2 - x - 4\)
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) \(\dfrac{1}{4}, -1\)
(ii) \(\sqrt{2}, \dfrac{1}{3}\)
(iii) \(0, \sqrt{5}\)
(iv) \(1, 1\)
(v) \(-\dfrac{1}{4}, \dfrac{1}{4}\)
(vi) \(4, 1\)