Since we don't know how many numbers multiply to 4 and the same on addition give -6.
Let us say there are n variables which are:
a1, a2, a3,..., an.
According to question:
a1 x a2 x a3 x... x an = 4
a1 + a2 + a3 + ... + an = -6
We obtain two equations.
Solution to the problem can be obtained only if the number of variables = number of equations.
Since we have only two equations so the number of variables should be 2.
So we can answer to the problem we have these two equations:
a1 x a2 = 4.....(1)
a1 + a2 = -6....(2)
From equation 2 we have a1 = -6 - a2
Putting a1 = -6 - a2 in equation we get:
(-6 - a2) x a2 = 4
-6a2 - a22 = 4
a22 + 6a2 + 4 = 0 which is a quadratic equation in one variable.
General form is: px2 + qx + r = 0
And its solution is: x = [-q ± (q2 - 4pr)1/2]/2p
On comparing we get p = 1, q = 6 and r = 4
And solution is: a2 = [-6 ± (62 - 4x1x4)1/2]/2 = -3 ±√5
When a2 = -3 - √5 then a1 = - 6 - (-3 - √5) = -3 + √5
When a2= -3 + √5 then a1 = -6 - (-3 + √5) = -3 - √5
-4 and -2
6 and -1
78
22
-16
15
The numbers are: 20 and -6
9
12
50
15
The numbers that add up to negative 6 and multiply to negative 27 are -3 and 9.