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I've got an equation like this and I want to calculate the roots of this equation. I've tried to solve it with the quadratic equation but I'm struggling to find the quadratic formula's $a, b$, and $c$ values.

$$ f(x) =\dfrac{-F_1^2F_2^2x^2-200000000F_1F_2R_1x+10000F_1F_2F_3R_1R_2-10000000000000000R_1^2}{F_1^2F_2^2x^2+200000000F_1F_2R_1x+10000000000000000R_1^2} $$

I've thought that since the equation is in $ax^2 + bx + c$ forma

t, $f(0)$ could return the $c$ value and I also could find the other $a$ and $b$ values with $f(1)$ and $f(-1)$ values. I'm not sure if the result is right or not through. Do you think that this method can work? If it won't, what is the proper way to find $a, b$ and $c$ values for a complicated equation like this ? Thanks!

(PS: $F$ and $R$ values are constants.)

tarik0
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  • A quadratic polynomial is something of the form $ax^2+bx+c$. What you have is of the form ${ax^2+bx+c\over dx^2+ex+f}$, which is completely different; you don't have a quadratic polynomial. Now, when you ask for "the roots of this equation", I take it you mean, you want to find the values of $x$ that make $f(x)=0$. Well, a quotient is zero implies the numerator is zero, and your numerator is a quadratic polynomial, so you can just apply the quadratic formula to it, and ignore the denominator entirely (well, not entirely, as you have to check whether it has a common zero with the numerator). – Gerry Myerson Dec 04 '22 at 01:44
  • Thanks a lot! I was a bit confused about what I was dealing with. – tarik0 Dec 04 '22 at 19:16

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