Video narration
You find two answers in a quadratic-but why are they called zeroes? Without the meaning, it feels like the calculation just ends. Think of a polynomial as an input-output machine, like a calculator. You enter x, and it produces p(x). A zero is an input that makes the output zero. Use factorisation: p(x) = x2 − 5x + 6 = (x − 2)(x − 3). For zero output, either x − 2 or x − 3 must be zero. So the zeroes are 2 and 3. Here's the flip: they are not isolated exam answers. They describe the machine. Their sum is 2 + 3 = 5, and their product is 2 × 3 = 6. For a quadratic ax2 + bx + c, the coefficients encode this pattern: sum equals −b/a, and product equals c/a. Zeroes are the inputs that make the polynomial output zero. And this machine's coefficients carry their sum and product.