Question

Solve each equation. $$ x^{2}-3 x-10=0 $$

   Solve each equation.
$$
x^{2}-3 x-10=0
$$

Algebra for College Students

Algebra for College Students

Margaret L. Lial,… 9th Edition

Chapter 5, Problem 11

Instant Answer

Solved by Expert Juhi Singh

02/24/2022

Step 1

We are looking for two numbers that multiply to -10 and add to -3. The numbers -5 and 2 satisfy these conditions. So, we can write the equation as: $$ x^{2}-3 x-10=(x-5)(x+2)=0 $$ Show more…

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Solve each equation. $$ x^{2}-3 x-10=0 $$

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Key Concepts

Zero-Product Property

The zero-product property states that if a product of two or more factors is zero, then at least one of the factors must be zero. This property is crucial in solving factored quadratic equations, as it allows each factor to be set equal to zero to find the solutions.

Factoring

Factoring involves rewriting a polynomial as a product of simpler expressions, known as factors. In the context of quadratic equations, one looks for two binomials whose product equals the original expression, which can simplify the process of finding its roots.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation typically written in the form ax² + bx + c = 0. Its solutions can be found using various methods such as factoring, completing the square, or applying the quadratic formula.

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