
### Instruction: help me answer this question If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation., think step by step
### Assistant: Let the roots of the quadratic equation be a and b. Given the arithmetic mean (A.M.) and geometric mean (G.M.) of the roots, we can use the properties of A.M. and G.M. to determine the values of (a + b) and ab. Subsequently, we can form a quadratic equation using the formula x<sup>2</sup> - x(a + b) + (ab) = 0. , The answer is The quadratic equation is x<sup>2</sup> - 16x + 25 = 0.
