Question

Solve each equation. See Examples $1-5$ $$x^{2}-3 x-10=0$$

   Solve each equation. See Examples $1-5$
$$x^{2}-3 x-10=0$$

Intermediate Algebra

Intermediate Algebra

Margaret L. Lial,… 11th Edition

Chapter 6, Problem 7

Instant Answer

Solved by Expert Heather Zimmers

07/25/2020

Step 1

The equation is $x^{2}-3 x-10=0$. We can factor this into $(x-5)(x+2)=0$. Show more…

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Solve each equation. See Examples $1-5$ $$x^{2}-3 x-10=0$$

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Key Concepts

Factorization

Factorization is a method used to solve quadratic equations by expressing the quadratic expression as a product of two binomials. When the expression can be factored, each binomial is set equal to zero, leading directly to the solutions of the equation. This method is efficient when the quadratic readily factors into simple integer expressions.

Zero Product Property

The zero product property is a fundamental principle in algebra which states that if a product of two or more factors equals zero, then at least one of the factors must be zero. This property is crucial in solving factored quadratic equations because once the quadratic is expressed as a product, each factor can be set to zero to determine the potential solutions.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a, b, and c are constants and a is not zero. Solving quadratic equations involves finding the values of the variable that make the equation true, which can be approached through various methods including factoring, completing the square, and using the quadratic formula.

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