What multiplies to be 4 but adds to be negative 6?

Answer 1

10

Answer 2

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

Answer 3

Oh, what a delightful little puzzle we have here! Let's see, if we're looking for two numbers that multiply to be 4 and add up to be -6, we can think of -2 and -2. Yes, that's right! -2 times -2 is 4, and -2 plus -2 is indeed -4. Just remember, mistakes are just happy little accidents in the world of math!