Questions: Solve x^2-5x+6=0

Solve x^2-5x+6=0
Transcript text: Solve \[ x^{2}-5 x+6=0 \]
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Solution

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To solve the quadratic equation \(x^2 - 5x + 6 = 0\), we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the equation \(ax^2 + bx + c = 0\).

Paso 1: Identificar los coeficientes de la ecuación cuadrática

Dada la ecuación cuadrática \(x^2 - 5x + 6 = 0\), identificamos los coeficientes:

  • \(a = 1\)
  • \(b = -5\)
  • \(c = 6\)
Paso 2: Calcular el discriminante

El discriminante de una ecuación cuadrática \(ax^2 + bx + c = 0\) se calcula como: \[ \Delta = b^2 - 4ac \] Sustituyendo los valores: \[ \Delta = (-5)^2 - 4 \cdot 1 \cdot 6 = 25 - 24 = 1 \]

Paso 3: Calcular las soluciones usando la fórmula cuadrática

La fórmula cuadrática es: \[ x = \frac{-b \pm \sqrt{\Delta}}{2a} \] Sustituyendo los valores: \[ x_1 = \frac{-(-5) + \sqrt{1}}{2 \cdot 1} = \frac{5 + 1}{2} = \frac{6}{2} = 3 \] \[ x_2 = \frac{-(-5) - \sqrt{1}}{2 \cdot 1} = \frac{5 - 1}{2} = \frac{4}{2} = 2 \]

Respuesta Final

Las soluciones de la ecuación cuadrática \(x^2 - 5x + 6 = 0\) son: \[ \boxed{x_1 = 3} \] \[ \boxed{x_2 = 2} \]

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