Show that the fundamental theorem of algebra is true for the quadratic polynomial x^2 - 16x + 39 = 0 through solving by factoring. which of the following statements accurately describes the solution set?

Question

Show that the fundamental theorem of algebra is true for the quadratic polynomial x^2 - 16x + 39 = 0 through solving by factoring. which of the following statements accurately describes the solution set?

these are two irrational solutions

there are two non-real solutions

there are two rational solutions

there two identical solutions

Answer 1

To solve the quadratic equation x^2 - 16x + 39 = 0, we can factor it as (x - 3)(x - 13) = 0. This implies that either (x - 3) = 0 or (x - 13) = 0.

If (x - 3) = 0, then x = 3.

If (x - 13) = 0, then x = 13.

So the solution set for the equation x^2 - 16x + 39 = 0 is {3, 13}.

Both of these solutions are rational numbers, so the accurate statement that describes the solution set is: "There are two rational solutions."