Daniel Carrión: Solving Quadratic Equations of Second Degree

¿Cuáles son los coeficientes de la ecuación cuadrática 3x² - 2x = 4?

¿La fórmula para resolver ecuaciones cuadráticas de la forma x² + bx + c = 0 es x = -b/2 ± √(b²-4ac)/2a?

¿La ecuación x² + 2x + 8 = 0 se resuelve utilizando la fórmula cuadrática?

¿El valor de x1 al resolver la ecuación x² + 2x + 8 = 0 es 4?

¿La fórmula cuadrática proporciona solo una solución para una ecuación de segundo grado?

Daniel Carrión: speaking about solving quadratic equations of second degree
Quadratic equation: form where x appears at least once squared, e.g. x² + 12x + 8 = 0
Terms:
- Coefficient of the quadratic term (x²): a
- Coefficient of the linear term (x): b
- Constant term (without x): c
Examples:
- 3x² - 2x = 4: a = 3, b = -2, c = 4
- 6x² + 3x - 5 = 0: a = 6, b = 3, c = -5
- x² + 5x + 8 = 0: a = 1, b = 5, c = 8
Formula to solve quadratic equations of the form x² + bx + c = 0
- x = -b/2 ± √(b²-4ac)/2a
Solving a quadratic equation involves finding the value of x
In the provided example, x² + 2x + 8 = 0 is to be solved.
Determining values of a, b, and c: a = 1, b = 2, c = -8
Applying the quadratic formula: x = -2 ± √(2²-4(1)(-8)/2(1))
Solving for x1: x = -2 + √(16+32) = 4
Solving for x2: x = -2 - √(16+32) = -10
The quadratic formula provides two solutions, one for the positive sign and the other for the negative sign.
In the given example, x = 4 and x = -10 are the solutions.

This quiz covers the process of solving quadratic equations of the form x² + bx + c = 0, as demonstrated by Daniel Carrión. It explains the terms involved, such as coefficients of the quadratic and linear terms, and the constant term. It also includes examples and the application of the quadratic formula.