basic algebra

[vaibhav101]

if the equations $$ax^2+bx+c=0$$ and $$cx^2+bx+a=0$$ have a negative common root then the value of (a-b+c) is
A 0
B 2
C 1
D -1
E none

[deloitte247]

Let "d" be the common root of the two equation
$$ad^2+bd+c=0\ \ \ \ \ \ \ and\ $$
$$cd^2+bd+a=0$$
$$\left(\frac{d^2}{ab-c^2}\right)=\frac{d}{bc-a^2}=\frac{1}{ac-b^2}$$
$$d=\frac{\left(bc-a^2\right)}{\left(ac-b^2\right)}$$
$$\left(cb-a^2\right)^2=\left(ab-c\right)\left(ac-b^2\right)$$
$$a^3+b^3+c^3=3abc$$
$$a^3+b^3+c^3-3abc=0$$
$$\left(a+b+c\right)\left(a^2+b^{2+}c^2-ab-ac-bc\right)=0$$
$$a^2+b^{2+}c^2=0$$
$$a^2+b^{2+}c^2-ab-ac-bc=0$$
$$a+b+c=0$$
Option A is the answer