Originally Posted by
HallsofIvy There is something of an ambiguity about the term "roots". I learned that an equation has roots while a polynomial has zeros. Specifically, the zeros of the polynomial p(x) are the roots of the equation p(x)= 0. Strictly speaking, then, you can talk about the "roots" of the equation $\displaystyle 3x^2- 3= 0$, or the "zeros" of the polynomial $\displaystyle 3x^2- 3$. But students tend to use "root" and "zero" interchangebly. In either case, since $\displaystyle 3x^2- 3= 0$ is the same as $\displaystyle 3x^2= 3$ and, dividing both sides by 3, $\displaystyle x^2= 1$, the roots are indeed x= 1 and x= -1. As mr fantastic suggested, have your friend replace x in the equation by 1.7 and see what happens. He should get approximately "6", not "0".