Answer:
-8
Step-by-step explanation:
For roots r and s, the quadratic can be factored ...
f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs
Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...
r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2
Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...
(x-coefficient)^2 -2(constant term)
we get ...
r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6
r^2 +s^2 = 2(m -1)^2 -8
The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.
Each cat would get 1/20 of the whole bag of cat food.
Answer:
Step-by-step explanation:
Given that When n is divided by 21, the remainder is an odd number.
i.e. 
where m is an integer and k a positive integer <21
When n is divided by 28, the remainder is 3
, where c is a positive integer
This can be written as
Since n is giving odd remainder when divided by 21,
we get r =3 as n is a multiple of 7 +3
