Mathematics

The discriminant tells you whether a quadratic has real roots or complex ones—it's the "gatekeeper" under the square root in the quadratic formula. For any equation $ax^2 + bx + c = 0$, compute $\Delta = b^2 - 4ac$: if it's positive, you get two distinct real roots; if zero, one repeated real root; if negative, two complex conjugate roots. Here you just need to identify $a$, $b$, and $c$, plug them in, and interpret what the sign tells you.

The discriminant tells you whether a quadratic has real roots or complex ones—it's the "gatekeeper" under the square root in the quadratic formula. For any equation $ax^2 + bx + c = 0$, compute $\Delta = b^2 - 4ac$: if it's positive, you get two distinct real roots; if zero, one repeated real root; if negative, two complex conjugate roots. Here you just need to identify $a$, $b$, and $c$, plug them in, and interpret what the sign tells you.