Question

What equals 5 in multiplication and -4 in addition

Answer 1

Answer:

• -2 +i
• -2 -i

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.