The expression I would like to find the zero of is: $$ -407\,x^{2} + 220275\,x - 6118.75\,ax - 15296.875\,a^{2} + 1101375\,a - 19824750 $$ I would like to express the zero in terms of $a$, I have tried doing it myself but been getting stuck. I am trying to find the zero in terms of $a$ so that I will be able to interpret the minimum of a different function for various $a$ values.
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1Collect the terms then it's just a quadratic equation in $x$. – dxiv May 07 '17 at 01:49
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If $$k_1 x^2 + (k_2+ak_3)x+f(a)=0$$ then $$x=\frac{-(k_2+ak_3)\pm \sqrt{(k_2+ak_3)^2 - 4k_1f(a)}}{2k_1} $$
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