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I am reading Lehman's Mathematics for Computer Science. In chapter 16 Generating Functions.enter image description here enter image description here I couldn't see how $1-x-x^2 = (x-r_1)(x-r_2)$. Shouldn't it be $1-x-x^2 = -1(x-r_1)(x-r_2)$? Since $r_1 r_2 = r_1+r_2 = -1$, $1-x-x^2 = -1(x-r_1)(x-r_2) = (1-x/r_1)(1-x/r_2)$?

光復香港 時代革命 Free Hong Kong
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Sean
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    I don't have the book but both $1-x-x^2$ and $x^2+x-1$ have the same roots (cross the x-axis) in the same place. Apply the quadratic formula to each to see this. Each is a reflection of the other in the $x$-axis. So, if you only care about the roots, and not which parabola gave them, it doesn't matter which you use. – Martin Hansen Nov 19 '21 at 21:06

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Yes, you're right. This is a typo. It should be $-(x-r_1)(x-r_2)$.

Markus Scheuer
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