Given the sum and product of the Roots, Find the equation of the quadratic equation. Show your complete solution, 1.) Sum = 3√2 Product = 3 2.) Sum = -4/7 Product=2√7 3.) Sum = 3.15 Product = 1.2 4.) Sum = -12√17 Product = 5√3 5.) Sum = 1/17 Product = 5/246.) Sum = 5.12 Product = 24.3​

Answer:To find the quadratic equation given the sum and product of its roots, you can use the general form of a quadratic equation:ax^2 + bx + c = 0where the sum of the roots is -\frac{b}{a} and the product of the roots is \frac{c}{a}. For simplicity, we use a = 1, so the equation becomes:x^2 - (\text{Sum of roots})x + (\text{Product of roots}) = 0Let’s apply this to each case:1. **Sum = 3\sqrt{2}, Product = 3** The quadratic equation is: x^2 - (3\sqrt{2})x + 3 = 02. **Sum = -\frac{4}{7}, Product = 2\sqrt{7}** The quadratic equation is: x^2 - \left(-\frac{4}{7}\right)x + 2\sqrt{7} = 0 x^2 + \frac{4}{7}x + 2\sqrt{7} = 03. **Sum = 3.15, Product = 1.2** The quadratic equation is: x^2 - 3.15x + 1.2 = 04. **Sum = -12\sqrt{17}, Product = 5\sqrt{3}** The quadratic equation is: x^2 - (-12\sqrt{17})x + 5\sqrt{3} = 0 x^2 + 12\sqrt{17}x + 5\sqrt{3} = 05. **Sum = \frac{1}{17}, Product = \frac{5}{24}** The quadratic equation is: x^2 - \frac{1}{17}x + \frac{5}{24} = 06. **Sum = 5.12, Product = 24.3** The quadratic equation is: x^2 - 5.12x + 24.3 = 0

Answered by touyakyoji | 2024-09-06