Question

What two numbers can add to 4 but multiple to -12

Answer 1

Numbers: 6 and -2

Explanation:

Equations

This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.

However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:

`x+y=4\qquad\qquad [1]`

`x.y=-12\qquad\qquad [2]`

Solving [1] for y:

`y=4-x`

Substituting in [2]

`x(4-x)=-12`

Operating:

`4x-x^2=-12`

Rearranging:

`x^2-4x-12=0`

Solving with the quadratic formula:

`\displaystyle x=(-b\pm √(b^2-4ac))/(2a)`

With a=1, b=-4, c=-12:

`\displaystyle x=(-(-4)\pm √((-4)^2-4(1)(-12)))/(2(1))`

`\displaystyle x=(4\pm √(16+48))/(2)`

`\displaystyle x=(4\pm 8)/(2)`

The solutions are:

`\displaystyle x=(4+ 8)/(2)=6`

`\displaystyle x=(4- 8)/(2)=-2`

This confirms the preliminary results.

Numbers: 6 and -2