Solve the given quadratic equations by factoring. 2 x^2-7 a...

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0. It represents one of the most common types of equations in algebra and its solutions can often be found using methods such as factoring, completing the square, or the quadratic formula.

Standard Form

Expressing an equation in standard form means rewriting it as ax² + bx + c = 0. This is a crucial step before applying solution methods like factoring because it clearly identifies the coefficients and constant term, making the structure of the quadratic explicit.

Factoring Techniques

Factoring involves rewriting the quadratic expression as a product of two binomials. This method relies on finding two numbers that multiply to give the product of the coefficient of x² and the constant term and add up to the coefficient of x. This technique allows one to break down the quadratic expression into simpler multiplicative components.

Zero Product Property

The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. This principle is employed after factoring a quadratic equation; by setting each factor equal to zero, one can find the roots of the original equation.

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