SOLUTION: what two numbers add to -4 and multiply to 5

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Question 1204191: what two numbers add to -4 and multiply to 5
Found 3 solutions by math_tutor2020, josgarithmetic, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): 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.
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
"Multiply to 5"?
1*5, (-1)(-5)
"add to -4"?

NO.
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.

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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