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polynomial_function [2016/09/28 18:39] nikolaj |
polynomial_function [2016/10/11 13:13] nikolaj |
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| === Discussion === | === Discussion === | ||
| + | == Simply quadratic equation == | ||
| $q(x)=x\,x-a\,x$ | $q(x)=x\,x-a\,x$ | ||
| - | $q(x)=0 \implies x=a$ | + | $q(x)=0 \implies (x=0\lor x=a)$ |
| + | == A small deviation == | ||
| $p(x)=x\,x-a\,x+b$ | $p(x)=x\,x-a\,x+b$ | ||
| $p(x)=0 \implies x=a\cdot\dfrac{1+\epsilon\sqrt{1-\left(\frac{2}{a}\right)^2\cdot b}}{2}, \epsilon=\pm 1$ | $p(x)=0 \implies x=a\cdot\dfrac{1+\epsilon\sqrt{1-\left(\frac{2}{a}\right)^2\cdot b}}{2}, \epsilon=\pm 1$ | ||
| + | |||
| + | $\lim_{b\to 0}\sqrt{1-\left(\frac{2}{a}\right)^2\cdot b}=1$ | ||
| <code> | <code> | ||
