$$ax^2 + bx + c = 0\quad\text{and}\quad
bx^2 + cx + a = 0$$
have a common root.
In my book, it says that 1 is a common root for those equation?
Is this correct.
When we plug 1 in both the equations, we get $a+b+c = 0$, it says nothing about 1 being a root. Since we don't know if LHS is zero or not.
Where I'm going wrong here?
Best Answer
From first one you have $$c=-ax^2-bx$$ so put this in second eqaution and you get:$$ ax^3-a=0$$ Since $a\neq 0$ we have $x=1$ or solution of $x^2+x+1=0$.