Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Equations
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. The solutions to this equation, known as the roots, can be found using various methods, including factoring, completing the square, or applying the quadratic formula. Understanding the structure of quadratic equations is essential for solving them.
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Zero-Product Property
The zero-product property states that if the product of two factors equals zero, then at least one of the factors must be zero. This principle is crucial when solving quadratic equations by factoring, as it allows us to set each factor equal to zero to find the solutions. In this context, it helps in determining the values of a, b, and c when given specific roots.
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Factoring Quadratics
Factoring quadratics involves expressing the quadratic equation in the form (x - r1)(x - r2) = 0, where r1 and r2 are the roots of the equation. This method simplifies finding the coefficients a, b, and c by relating them to the roots. For example, if the roots are known, the equation can be expanded to identify the corresponding coefficients.
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