. Find f(x).

Question

Suppose that the function f(x) is a quadratic function with roots at x=2-3i and x=2+3i. Find f(x).

Answer 1

Formula : If a and b are two roots ot the quadtratic equation and sum of the roots = a + b and product of roots = ab then the quadratic equation is x^2 - (a + b)x + ab =  0 ------------> (1)

Given roots are a = (2-3i) and b = (2+3i)

Sum of the roots = (2 - 3i) + (2 + 3i)

                           =  4

Product of the roots  =  (2 - 3i)(2 + 3i)

                                  =  (2^2) - (3i)^2

                                  =  4 - 9(i)^2

                                  =  4 - 9(-1)

                                  =  4 + 9

                                  =  13

Substitute corresponding values in Eq (1)

x^2 - 4x + 13  =  0

Answer :

The quadratic equation is x^2 - 4x + 13  =  0.