This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The roots of the equation x^2 - 5x + 6 = 0 are x=2 and x=3. Steps: 1. Identify the coefficients: For a quadratic equation in the form ax^2 + bx + c = 0, we have: a = 1 b = -5 c = 6 2. Write the quadratic formula: The quadratic formula is given by: x = -b ± sqrt(b^2 - 4ac)2a 3. Substitute the values into the formula: x = -(-5) ± sqrt((-5)^2 - 4(1)(6))2(1) 4. Simplify the expression: x = 5 ± sqrt(25 - 24)2 x = 5 ± sqrt(1)2 x = (5 ± 1)/(2) 5. Calculate the two roots: For the positive sign: x_1 = (5 + 1)/(2) = (6)/(2) = 3 For the negative sign: x_2 = (5 - 1)/(2) = (4)/(2) = 2 The roots of the equation x^2 - 5x + 6 = 0 are x=2 and x=3.