Final answer:
To find two numbers whose product is -12 and their sum is -1, we can solve a system of equations. The two numbers are 3 and -4 or -4 and 3.
Step-by-step explanation:
To find two numbers whose product is -12 and their sum is -1, we can set up a system of equations. Let's assume the two numbers are x and y.
From the given information, we have the following equations:
Equation 1: xy = -12
Equation 2: x + y = -1
We can solve this system of equations by substitution or elimination. Let's use substitution:
From Equation 2, we can rewrite it as:
y = -1 - x
Substituting this value of y into Equation 1:
x(-1 - x) = -12
Simplifying:
-x - x² = -12
Rearranging terms:
x² + x - 12 = 0
Factoring:
(x - 3)(x + 4) = 0
Setting each factor equal to zero:
x - 3 = 0 or x + 4 = 0
So we have two possible values for x:
x = 3 or x = -4
Substituting these values back into Equation 2, we can find the corresponding values of y:
If x = 3, y = -1 - 3 = -4
If x = -4, y = -1 - (-4) = 3
Therefore, the two numbers are 3 and -4 or -4 and 3.
Learn more about Solution of Equations