Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

(i) 1/4, -1

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(1/4)x -1  = 0

Multiply by 4 to remove denominator we get

4x²  -  x  -4  = 0

(ii) √2 , 1/3

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(√2)x  + 1/3  = 0

Multiply by 3 to remove denominator we get

3x²  - 3√2 x + 1  = 0

(iii)  0, √5

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(0)x  + √5  = 0

simplify it we get

x²   + √5  = 0

(iv) 1, 1

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(1)x  + 1  = 0

simplify it we get

x²  -  x + 1  = 0

(v) -1/4 ,1/4

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(-1/4)x  + 1/4  = 0

multiply by 4 we get

4x²   +  x + 1  = 0

(vi) 4, 1

Now formula of quadratic equation is

x²-(Sum of root)x + (Product of root) = 0

Plug the value in formula we get

x² –(4)x  + 1 = 0

x² - 4x + 1 = 0