Question

find a quadratic polynomial, whose sum and product of zeroes are 3 and 3/2 respectively

Answer 1

A quadratic equation is of the form

${x}^{2} - (sum \: of \: roots)x + product \: of \: roots \: = 0$
Given that,
sum of roots = 3
product of roots = 3/2
So,

${x}^{2} - 3x + \frac{3}{2} = 0 \\ = > \frac{2 {x}^{2} - 6x + 3}{2} = 0 \\ = > 2 {x}^{2} - 6x + 3 = 0$
Therefore,the quadratic equation is
$2 {x}^{2} - 6x + 3 = 0$