Question

Solve the equation by factoring. $$2 y^{2}+5 y-3=0$$

   Solve the equation by factoring.
$$2 y^{2}+5 y-3=0$$

Contemporary Precalculus

Contemporary Precalculus

Thomas W.… 5th Edition

Chapter 1, Problem 17

Instant Answer

Solved by Expert Charles Carter

07/18/2020

Step 1

To do this, we multiply the first and last terms (2 and -3) to get -6. We then look for two numbers that multiply to -6 and add to 5. These numbers are 6 and -1. So, we rewrite the equation as: $$2 y^{2}+6 y-y-3=0$$ Show more…

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Solve the equation by factoring. $$2 y^{2}+5 y-3=0$$

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Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically written in the standard form ax² + bx + c = 0. They play a fundamental role in algebra and are used to model various phenomena. Understanding the structure of quadratic equations is essential for determining the most appropriate method for finding their solutions.

Factoring

Factoring is a technique used to express a polynomial as a product of two or more simpler polynomials. In the context of quadratic equations, this method involves rewriting the quadratic expression as a product of two binomials. Factoring is particularly useful because it can simplify the process of solving equations by reducing them to lower-degree factors.

Zero Product Property

The zero product property is a key algebraic principle stating that if the product of two or more factors equals zero, at least one of the factors must be zero. This property is crucial when solving factored quadratic equations, as it allows each factor to be set equal to zero, leading directly to the solutions of the equation.

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