Solve the given quadratic equations by factoring. 3 x^2-13...

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Key Concepts

Zero Product Property

The zero product property states that if the product of two expressions equals zero, then at least one of the expressions must be zero. This principle is crucial when solving equations that have been factored, as it allows each factor to be set equal to zero to determine the solution set.

Solution Verification

Verifying solutions by substituting them back into the original equation ensures that they satisfy the equation. This step is important to confirm that the factoring process was correctly executed and that no extraneous solutions were introduced.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation usually written in the form ax² + bx + c = 0. These equations are fundamental in algebra and appear in various applications, including physics and engineering, where their solutions represent important values such as projectile paths or optimization conditions.

Factoring

Factoring is the process of rewriting a polynomial as a product of simpler binomials or polynomials. When successful, factoring transforms a quadratic equation into a product of two linear factors, facilitating a straightforward route to finding the equation's roots.

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