Si \( x^2 - 5x + 6 = 0 \), quelle est la somme des solutions pour \( x \)?

["SEO Optimized Article: Solving the Quadratic Equation ( x^2 - 5x + 6 = 0 ) and Finding the Sum of Solutions", "---", "Understanding how to solve quadratic equations is a fundamental skill in algebra, essential for students and math enthusiasts alike. One classic example is the equation ( x^2 - 5x + 6 = 0 ). In this article, we explore the solutions to this equation and reveal a powerful insight: the sum of the solutions.", "### Solving the Equation ( x^2 - 5x + 6 = 0 )", "This quadratic equation can be solved in several ways—factoring, completing the square, or using the quadratic formula. For this equation, factoring is the clearest and most efficient method.", "We seek two numbers that multiply to the constant term ( 6 ) and add up to the coefficient of ( x ), which is ( -5 ).", "Looking at factor pairs of 6:", "- ( 1 \ imes 6 = 6 ) and ( 1 + 6 = 7 ) (too high)\n- ( 2 \ imes 3 = 6 ) and ( 2 + 3 = 5 )\n- Negative pairs: ( (-2) \ imes (-3) = 6 ) and ( -2 + (-3) = -5 ) ✅", "So, we factor the quadratic as:\n[\nx^2 - 5x + 6 = (x - 2)(x - 3) = 0\n]", "Setting each factor equal to zero gives the solutions:\n[\nx - 2 = 0 \Rightarrow x = 2\n]\n[\nx - 3 = 0 \Rightarrow x = 3\n]", "Thus, the solutions are ( x = 2 ) and ( x = 3 ).", "### The Sum of the Solutions", "Beyond simply finding individual roots, a powerful algebraic property helps us determine the sum of the solutions without solving the equation directly.", "For any quadratic equation in the standard form:\n[\nax^2 + bx + c = 0\n]\nthe sum of the solutions ( x_1 + x_2 ) is given by:\n[\nx_1 + x_2 = -\frac{b}{a}\n]", "In our equation ( x^2 - 5x + 6 = 0 ):\n- ( a = 1 )\n- ( b = -5 )", "So,\n[\nx_1 + x_2 = -\frac{-5}{1} = 5\n]", "This matches our direct solution: ( 2 + 3 = 5 ).", "### Why This Property Matters", "Using the formula ( -\frac{b}{a} ) saves time and reduces errors, especially for complex equations. It confirms that regardless of how we solve the quadratic—factoring, completing the square, or applying the quadratic formula—the sum remains consistently 5.", "---", "Conclusion:\nThe equation ( x^2 - 5x + 6 = 0 ) has solutions ( x = 2 ) and ( x = 3 ). The sum of these solutions is ( 5 ), a result that aligns with the elegant algebraic identity ( x_1 + x_2 = -\frac{b}{a} ). Mastering this concept not only simplifies computations but also deepens understanding of quadratic behavior across algebra and higher mathematics.", "Keywords: ( x^2 - 5x + 6 = 0 ), solutions, sum of solutions, quadratic equation, algebra, factoring, Vieta’s formula, mathematics tutorial", "Meta Description:\nLearn how to solve ( x^2 - 5x + 6 = 0 ) and discover why the sum of its solutions is always 5 using the identity ( x_1 + x_2 = -\frac{b}{a} ). Perfect for students and math learners.", "---", "Optimize your quadratic equation skills and unlock deeper mathematical insights — start with the sum of solutions!"]