If the equations a$x^2$ +bx+ c = 0 and c$x^2$ +bx+ a= 0, a $\ne$ c have a negative common root, then find the values of a- b + c.

$\begin{array}{l}{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0 ... \left(\mathrm{i}\right)\\ {\mathrm{cx}}^2+\mathrm{bx}+\mathrm{a}=0 ... \left(\mathrm{iI}\right)\end{array}$

(i) - (ii), we get, (a - c)x² = (a - c) 

x² = 1 

x = 1 

x =-1 Hence, the value of a-b+c=0