Question

Solve each equation. $$ 2 x^{3}-9 x^{2}-5 x=0 $$

   Solve each equation.
$$
2 x^{3}-9 x^{2}-5 x=0
$$

Algebra for College Students

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 5, Problem 41

Instant Answer

Solved by Expert Juhi Singh

02/23/2022

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This gives us: $$ x(2x^{2}-9x-5)=0 $$ Show more…

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Solve each equation. $$ 2 x^{3}-9 x^{2}-5 x=0 $$

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Key Concepts

Zero Product Property

The zero product property states that if a product of factors equals zero, then at least one of the factors must be zero. This principle is commonly used after factoring an equation to set each individual factor equal to zero and solve for the variable.

Quadratic Formula

The quadratic formula is a method for solving second degree polynomial equations of the form ax^2 + bx + c = 0. Once a cubic polynomial is partially factored down to a quadratic factor, the quadratic formula can be applied to find its roots, ensuring that all solutions to the original equation are identified.

Factoring

Factoring is the process of rewriting an expression as a product of simpler expressions. In the context of polynomial equations, factoring can simplify the equation by extracting common factors or breaking down a higher degree polynomial into lower degree components, making it easier to isolate and solve for each variable factor.

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