Lesson 3 Year 10 Mathematics The Quadratic Formula

Factorising is a brilliant shortcut, but it only works if the solutions to a quadratic equation are "nice" numbers (rational). In the real world, the roots of a quadratic are more likely to be messy surds or decimals. For example, how would you factorise x^2 + 5x + 1 = 0? Y ou cannot. For these cases, we use human ingenuity's greatest algebraic gift: The Quadratic Formula. This formula works for *every* quadratic equation, no matter how complex. We will also learn about the Discriminant—a small part of the formula that acts like a "crystal ball," telling us how many solutions an equation has before we even start solving it.

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