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ehidna [41]
3 years ago
9

What factors multiply to -1 but add to 1

Mathematics
2 answers:
faltersainse [42]3 years ago
8 0
There are no such factors,therefore, you will have to use the quadratic formula. Plug it into the equation x=-b+/- sqrt(b^2-4ac)/2a.
juin [17]3 years ago
6 0
Let the two factors be x and y.
Two factors that multiply to -1: xy = -1
Two factors that add to 1: x + y = 1
From the second equation: x = 1-y
Plug x back into the first equation: (1-y)(y) = -1 \\ y-y^2 = -1 \\ y^2-y-1 = 0
There are no binomial pairs that result in this quadratic. Thus we must use the quadratic formula.
y^2-y-1=0 
\frac{-b+- \sqrt{b^2-4ac} }{2a}  \\ \\ \frac{1 +- \sqrt{1-4(1)(-1)} }{2} \\ \\  \frac{1 +- \sqrt{5} }{2}

x = -y = \frac{1 +- \sqrt{5} }{2}
Either x or y could be the positive factor. The other variable would have to be the negative factor.

Just a sidenote: \frac{1 +- \sqrt{5} }{2} is actually called the "Golden Ratio" because the ratio is found so often in beautiful example in nature. 
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