Answer:
Step-by-step explanation:
There is no pair of real numbers that have a total of -4 and a product of 5. The complex numbers (-2+i) and (-2-i) will meet your requirements.
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If the numbers of interest are 'a' and 'b', they will be zeros of the quadratic whose factored form is ...
(x -a)(x -b) = 0
Expanding that, we find an opportunity to use the given sum and product numbers:
x² -(a+b)x +ab = 0
x² -(-4)x +5 = 0
Rewriting this in vertex form gives ...
(x² +4x +4) +1 = 0
(x +2)² +1 = 0
We can find the values of x by subtracting 1 and taking the square root.
(x +2)² = -1
x +2 = ±√(-1) = ±i
x = -2±i
The two numbers of interest are -2+i and -2-i.
