Answer to Question #300980 in Algebra for golden

Question

why will f(x)= x/x^3-2x^2+5x have no zeros? ( THE SLASH IS A FRACTION SYMBOL, EVERYTHING BEFORE THE SLASH IS the nominator AND ANYTHING after the slash is the denominator. )

Answer 1

Solution:

$f(x)= \dfrac{x}{x^3-2x^2+5x} \\ \Rightarrow f(x)= \dfrac{x}{x(x^2-2x+5)} \\ \Rightarrow f(x)= \dfrac{1}{x^2-2x+5}$

To have zeroes, f(x) must be put equal to 0.

$f(x)= 0 \\\Rightarrow \dfrac{1}{x^2-2x+5}=0$

which cannot give any solution as LHS can never be 0.

Thus, no solution.