Question

Find quadraric polynomial where sum and product of the zeroes one a and 1/a

Answer 1

=>To form the quadratic equation the formula is:-

x²-(sum of roots)x+(product of roots)

so,here
sum of roots=a
product of roots=1/a

x²-ax+1/a

is the required quadratic equation!!

@Altaf

Answer 2

$Heya !!! \\ \\ This \: is \: your \: answer.$
$Given :-- \\ Sum \: of \: zeroes, \: \alpha + \beta = a. \\ Product \: of \: zeroes, \: \alpha \beta = \frac{1}{a}$
$We \: know \: that \: any \: quadratic \: \\ equation \: is \: of \: the \: form \\ p \: (x) = k {x}^{2} - ( \alpha + \beta )x + \alpha \beta$
$So \: by \: putting \: values, \\ p \: (x) \: = {x}^{2} - (a)x + \frac{1}{a} \\ = > {x}^{2} - ax + \frac{1}{a} = 0$
$Multiplying \: both \: sides \: by \: a, \: we \: get \\ a{x}^{2} - {a}^{2}x + 1 =0. \\ Hence \: the \: required \: fraction \: is \\ a{x}^{2} - {a}^{2}x + 1$