X2-4x+3=0

To solve the quadratic equation \(x^2 - 4x + 3 = 0\), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] For the equation \( ax^2 + bx + c = 0 \), we have: - \( a = 1 \) - \( b = -4 \) - \( c = 3 \) Substituting these values into the quadratic formula gives: \[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times 3}}{2 \times 1} \] \[ x = \frac{4 \pm \sqrt{16 - 12}}{2} \] \[ x = \frac{4 \pm \sqrt{4}}{2} \] \[ x = \frac{4 \pm 2}{2} \] This results in two solutions: 1. \( x = \frac{4 + 2}{2} = 3 \) 2. \( x = \frac{4 - 2}{2} = 1 \) Therefore, the solutions are \( x = 3 \) and \( x = 1 \).