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
Let's find the roots of the equation. The equation given is 2x^2 - 13x + 15 = 0. Step 1: Identify the coefficients of the quadratic equation. For a quadratic equation in the form ax^2 + bx + c = 0, we have: a = 2 b = -13 c = 15 Step 2: Use the quadratic formula to find the roots. The quadratic formula is x = -b ± sqrt(b^2 - 4ac)2a. Substitute the values of a, b, and c into the formula: x = -(-13) ± sqrt((-13)^2 - 4(2)(15))2(2) x = 13 ± sqrt(169 - 120)4 x = 13 ± sqrt(49)4 x = (13 ± 7)/(4) Step 3: Calculate the two possible roots. For the positive case: x_1 = (13 + 7)/(4) = (20)/(4) = 5 For the negative case: x_2 = (13 - 7)/(4) = (6)/(4) = (3)/(2) The roots of the equation are 5 and (3)/(2). Step 4: Compare the calculated roots with the given options. The options are: A. (5)/(2) B. (3)/(2) C. 5 D. 3 Both (3)/(2) (Option B) and 5 (Option C) are roots of the equation. Since this is a multiple-choice question and both are correct, we will select one of them. The correct option is B. The roots of the equation are B. (3)/(2) (and also C. 5). That's 2 down. 3 left today — send the next one.