Quadratic Equations — Core Skills

The core idea, one worked example, and short practice.

Written and reviewed by the Study Mondo Education TeamLast updated August 21, 2026

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Quadratic Equations: The Basics

A quadratic is an equation where the highest power of $x$ is $2$ , like $x^{2} + 7x + 12 = 0$ . To factor means to rewrite a sum as a multiplication. A solution, also called a zero or a root, is a value of $x$ that makes the equation true.

The one move is finding two numbers. For $x^{2} + bx + c$ , look for two numbers that multiply to $c$ and add to $b$ . In $x^{2} + 7x + 12$ , the numbers $3$ and $4$ multiply to $12$ and add to $7$ , so the factored form is $(x + 3)(x + 4) = 0$ .

Then use the zero rule: if two things multiply to zero, one of them must be zero. Set each parenthesis equal to zero and solve. Here $x = -3$ and $x = -4$ . Notice how the signs flip.

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The core idea, one worked example, and short practice.

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