If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$. If $-1$ is a root of $f(x)=0$, then the other root is $\dfrac{8}{5}$

Let the quadratic expression be f(x) = k(x+1)(x-r) because -1 is given as a root. Using f(1)+f(2)=0, we substitute x to get k(2)(1-r) + k(3)(2-r) = 0. Simplifying this gives 8 - 5r = 0, so the other root r is 8/5, which proves the assertion is correct. Since the reason merely states the same conclusion without showing the mathematical relationship derived from f(1)+f(2)=0, it does not adequately explain the assertion.

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