Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) 14, -1; (ii) √2, 1/3; (iii) 0, √5; (iv) 1, 1; (v) -1/4, 1/4; (vi) 4, 1

(i) 14, -1
Using the quadratic equation formula, x² - (Sum of roots)x + (Product of roots) = 0
Substitute the value in the formula, we get
x² - 14x - 1 = 0
(ii) √2, 1/3
Using the quadratic equation formula, x² - (Sum of roots)x + (Product of roots) = 0
Substitute the value in the formula, we get
x² - √2x + 1/3 = 0
Multiply by 3 to remove denominator,
3x² - 3√2x + 1 = 0
(iii) 0, √5
Using the quadratic equation formula, x² - (Sum of roots)x + (Product of roots) = 0
Substitute the value in the formula, we get
x² - 0x + √5 = 0
x² + √5 = 0
(iv) 1, 1
Using the quadratic equation formula, x² - (Sum of roots)x + (Product of roots) = 0
Substitute the value in the formula, we get
x² - 1x + 1 = 0
x² - x + 1 = 0
(v) -1/4, 1/4
Using the quadratic equation formula, x² - (Sum of roots)x + (Product of roots) = 0
Substitute the value in the formula, we get
x² - (-1/4)x + 1/4 = 0
Multiply by 4
4x² + x + 1 = 0
(vi) 4, 1
Using the quadratic equation formula, x² - (Sum of roots)x + (Product of roots) = 0
Substitute the value in the formula, we get
x² - 4x + 1 = 0