Question

find the quadratic equation whose sum and product of zeros are - 3 and 2

Answer 1

x= -3 and x= 2
x+3 = 0
x-2 = 0
(x+3)(x-2)=0 
x2+x-6=0 

Answer 2

Hey there !!

Let
$\alpha \: and \: \beta \:$
be the sum of zeroes and product of zeroes respectively

Then , Given that -

$\alpha + \beta \: = - 3 \\ \\and \: product \: of \: zeoes \: \alpha \beta \: = 2$
we know ,
$f(x) \: = k( {x}^{2} - ( \alpha + \beta ) x+ \alpha \beta ) \\ \\ putting \alpha + \beta = - 3 \: and \\ \alpha \beta = 2 \\ \\f(x) = {x}^{2} - ( - 3)x +(-3) 2 \\ = > f(x) = {x}^{2} + 3x -6$
Hope this helps u !!