Question

Solve using the quadratic formula. $$ -2 x_{2}+10 x-17=0 $$

   Solve using the quadratic formula.
$$
-2 x_{2}+10 x-17=0
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 9, Problem 69

Instant Answer

Solved by Expert Victor Salazar

02/04/2022

Step 1

In this case, we have a = -2, b = 10, and c = -17. Show more…

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Solve using the quadratic formula. $$ -2 x_{2}+10 x-17=0 $$

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Key Concepts

Discriminant

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It plays a crucial role in determining the nature of the roots of a quadratic equation. Specifically, if the discriminant is positive, there are two distinct real roots; if it is zero, there is one repeated real root; and if it is negative, the equation has two complex conjugate roots.

Complex Numbers

When the discriminant of a quadratic equation is negative, the square root of a negative number introduces the concept of complex numbers. In these cases, the roots of the quadratic equation are expressed in the form of complex numbers, which combine a real part and an imaginary part. Understanding complex numbers is essential when dealing with quadratics that do not have real solutions.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants. Understanding this form is fundamental because it allows one to identify the structure of the equation and to apply appropriate solution methods, such as factoring, completing the square, or using the quadratic formula.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac)) / (2a), provides a method for finding the roots of any quadratic equation. This formula is a universal solution that applies regardless of whether the quadratic is factorable, and it is derived by completing the square on the general quadratic equation.

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