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Double Root of a Quadratic Equation
A double root (also called a repeated root) occurs when a quadratic equation has two identical solutions. When the left side of a quadratic equation can be written as the product of two identical factors — such as — applying the Zero Product Property produces the same equation twice, so only one distinct value of the variable satisfies the equation. That single repeated value is called a double root.
For example, if solving a quadratic equation leads to both and , the solution appears twice. Rather than listing two separate solutions, the result is a single solution that counts with multiplicity two. Recognizing a double root is important because, unlike most quadratic equations that yield two different solutions, a squared-binomial equation equal to zero always yields exactly one solution.
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