You can put this solution on YOUR website!
This is something to do using trial-and-error.
It's implied that the numbers in question are integers.
Here's all of the ways to multiply to 5, using only integers.
1*5 = 5
(-1)*(-5) = 5
Luckily the list is really short.
Then we add up each pair
1+5 = 6
-1+(-5) = -6
We find that there aren't any pairs of numbers that add to -4 and multiply to 5.
This will mean x^2-4x+5 cannot be factored over the rational numbers.
If you wanted, you can use the quadratic formula to solve x^2-4x+5 = 0
Doing so leads to "no real number solutions" since the discriminant is negative.
This is further evidence there aren't pairs of integers that add to -4 and multiply to 5.
According to Vieta's theorem, these two numbers are the roots of the quadratic equation
x^2 + 4x + 5 = 0.
From here, it is easy to find these numbers
(x^2 + 4x + 4) + 1 = 0
= -1
x + 2 = = +/- i
x = -2 +/- i,
where "i" is the imaginary unit.
I understand that this answer is not what you are seeking for;
but in order for to get another answer, you should write your request in another form.
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