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
To find the sum of the roots of a quadratic equation, we first write the equation in the standard form ax^2 + bx + c = 0. The sum of the roots is given by the formula -(b)/(a). Step 1: Rewrite the given equation in standard form. The given equation is 6 - x - x^2 = 0. Rearranging the terms to match ax^2 + bx + c = 0: -x^2 - x + 6 = 0 To make the leading coefficient positive, we can multiply the entire equation by -1: x^2 + x - 6 = 0 Step 2: Identify the coefficients a, b, and c. From the equation x^2 + x - 6 = 0, we have: a = 1 b = 1 c = -6 Step 3: Calculate the sum of the roots. The roots are c and k, so their sum is c+k. Using the formula for the sum of the roots: c+k = -(b)/(a) Substitute the values of a and b: c+k = -(1)/(1) c+k = -1 The sum of the roots is -1. Comparing this with the given options: A. 2 B. 1 C. -1 D. -3 The correct option is C. The final answer is C. -1.