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 form a quadratic equation given its roots, we use the formula x^2 - (sum of roots)x + (product of roots) = 0. Step 1: Identify the given roots. Let the roots be = (2)/(sqrt(3)) and = sqrt(3). Step 2: Calculate the sum of the roots. + = (2)/(sqrt(3)) + sqrt(3) To add these, we find a common denominator: + = (2)/(sqrt(3)) + sqrt(3) · sqrt(3)sqrt(3) = (2)/(sqrt(3)) + (3)/(sqrt(3)) = (2+3)/(sqrt(3)) = (5)/(sqrt(3)) Rationalize the denominator: + = (5)/(sqrt(3)) · sqrt(3)sqrt(3) = 5sqrt(3)3 Step 3: Calculate the product of the roots. = (2)/(sqrt(3)) · sqrt(3) = 2 Step 4: Substitute the sum and product into the quadratic equation formula. The general form of a quadratic equation is x^2 - ( + )x + = 0. x^2 - (5sqrt(3)3)x + 2 = 0 Step 5: Clear the denominator by multiplying the entire equation by 3. 3 (x^2 - 5sqrt(3)3x + 2) = 3 · 0 3x^2 - 5sqrt(3)x + 6 = 0 The quadratic equation is: 3x^2 - 5sqrt(3)x + 6 = 0 Send me the next one 📸