Q.Verify whether $x = 3$ is a root of the equation $x^2 - x - 6 = 0$.

Substitute $x=3$ into the expression and check whether it evaluates to zero.

Let $p(x)=x^2-x-6$. Substitute $x=3$: $p(3)=(3)^2-(3)-6=9-3-6=0$.

Since $p(3)=0$, by the definition of a root (§2), $x=3$ is a root of the equation. …

Alternative — since $x=3$ is confirmed a root, the OTHER root follows from the product-of-roots relation $x_1 x_2 = \dfrac{c}{a} = \dfrac{-6}{1} = -6$: with $ …

A sign error is the most common failure here — e.g. computing $-x$ at $x=3$ as $+3$ instead of $-3$. Always substitute the value carefully term by term, keeping the sign of each coeffic …