Find the real solutions, if any, of each equation. Use the quadratic formula. x^2+4 x+2=0

Name: Problem 44, Chapter 1: Algebra and Trigonometry
Uploaded: 2020-07-06T15:32:55-08:00
Duration: 1 min 34 s
Channel: Tiffany Tran
Description: Find the real solutions, if any, of each equation. Use the quadratic formula. x^2+4 x+2=0

step 1 To use the quadratic formula, we know that this is going to be A. A is the one that's next to th

Find the real solutions, if any, of each equation. Use the...

Key Concepts

Real Solutions

In the context of quadratic equations, real solutions refer to answers that are real numbers, as opposed to complex numbers. Whether an equation has real solutions directly depends on the value of the discriminant, and the quadratic formula provides a clear criterion to check for the existence of real roots.

Discriminant

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, and it determines the nature of the roots of the quadratic equation. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution (a repeated root); and if it is negative, the equation has two complex conjugate solutions.

Quadratic Equation

A quadratic equation is a polynomial equation of degree two, typically expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a is non-zero. The solutions to a quadratic equation are the values of the variable that make the equation true and are found by various methods including factoring, completing the square, or using the quadratic formula.

Quadratic Formula

The quadratic formula is a universal method for solving quadratic equations and is derived from the process of completing the square. It states that the solutions to the equation ax² + bx + c = 0 are given by x = (-b ± ?(b² - 4ac)) / (2a), which allows for the systematic computation of the roots regardless of whether they factor neatly.

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