Given the equation of the parabola, for what values of $t$ will the quadratics have $0$, $1$, or $2$ solutions? Equation: $$0 = 3x^2 + tx + 10$$
Can you please explain the answer in simple terms, step by step if you can. How do I figure this out? I tried plugging in the $0$, $1$, and $2$ for the $x$ variables and solve for $t$ but that only gave me a correct solution for $0$ (when I plugged in $0$ $t$ had $0$ $x$ intercepts, but when I plugged in $1$ and later $2$, both had $2$ solutions so there must be something wrong there).