The shortcut almost nobody knows for certain quadratic equations

The quadratic formula always works, but it's not always necessary. Before diving in, take two seconds to look at the coefficients of your equation ax² + bx + c = 0.

If a + b + c = 0, then x = 1 is automatically a solution. And since the product of the two roots equals c/a, you find the second root with one division — no discriminant needed.

Example: 2x² - 5x + 3 = 0. Here a + b + c = 2 - 5 + 3 = 0, so x = 1 is a root. The other root is c/a divided by the first, which is 3/2.

A second useful reflex: if a - b + c = 0, then x = -1 is a root. Same logic, just the sign that changes.

These aren't magic tricks — they're direct consequences of the relationships between coefficients and roots you already see in class. But most students never take 5 seconds to check these two cases before jumping into the full formula. Make it a habit, and you'll save real time on the exam.