Question

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

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

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 12, Problem 76

Instant Answer

Solved by Expert Amy Jiang

09/01/2020

Step 1

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

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

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Key Concepts

Discriminant

The discriminant, given by b² - 4ac, is a component of the quadratic formula that reveals the nature and number of the roots. A positive discriminant indicates two distinct real roots, a zero discriminant indicates a repeated real root, and a negative discriminant indicates two complex conjugate roots.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), is a universal method for solving quadratic equations. It allows for direct computation of the roots regardless of whether the quadratic can be factored, and it is derived by completing the square on the standard form of the quadratic equation.

Factoring

Factoring is a method used to solve equations by expressing a polynomial as a product of simpler polynomials or factors. When the polynomial can be neatly factored, setting each factor equal to zero provides the solutions of the equation, making the process straightforward.

Quadratic Equation

A quadratic equation is any equation that can be written in the form ax² + bx + c = 0, where a, b, and c are constants and a is not zero. Understanding this standard form is crucial because it allows one to apply various solution strategies, such as factoring or the quadratic formula, to find the roots of the equation.

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