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

Explanation

(i) `1/4 = alpha + beta= -b/a`

`alpha*beta = -1= c/a`

for the equation `ax^2 + bx+c=0`

let a=4; `-b/a = 1/4`

`b=-1`

`c/4 = -1 => c=-4`

`p(x) = 4x^2 -x - 4`

(ii) `alpha+ beta= sqrt2 & alpha*beta = 1/3`

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