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1. To determine the value of the variable x in the quadratic equation represented by x^2 – 3x + 2 = 0, one must employ methods suitable for solving such equations. This particular equation is a standard form of a quadratic, where the coefficients can be identified as a = 1, b = -3, and c = 2. The solutions for x can be found using various techniques, including factoring, completing the square, or applying the quadratic formula, which is x = (-b ± √(b² – 4ac)) / (2a).
2. In this case, the equation can be factored directly. The expression x^2 – 3x + 2 can be rewritten as (x – 1)(x – 2) = 0. This factorisation indicates that the product of two binomials equals zero, which implies that at least one of the factors must be zero. Therefore, setting each factor to zero provides the potential solutions: x – 1 = 0 or x – 2 = 0. Solving these equations yields the values x = 1 and x = 2.
3. Understanding how to solve quadratic equations is a fundamental aspect of mathematics, particularly in the context of an A Level Maths Revision Course. Mastery of these concepts not only aids in solving similar problems but also lays the groundwork for more advanced mathematical studies. The ability to manipulate and solve equations such as x^2 – 3x + 2 = 0 is essential for students aiming to excel in their mathematical education and future applications in various fields.
