Question

Show that the Fundamental Theorem of Algebra is true for the quadratic polynomial x2−16x+39=0 through solving by factoring. Which of the following statements accurately describes the solution set?(1 point) Responses There are two irrational solutions. There are two irrational solutions. There are two rational solutions. There are two rational solutions. There are two non-real solutions. There are two non-real solutions. There are two identical solutions.

Answer 1

To solve the quadratic equation x^2 - 16x + 39 = 0 by factoring, we can look for two numbers whose product is 39 and sum is -16.

The factors of 39 are 1, 3, 13, and 39.
When we test the sums of these factors, we find that 13 + 3 = 16.

So, we can rewrite the quadratic equation as (x - 13)(x - 3) = 0.
This equation is satisfied when either x - 13 = 0 or x - 3 = 0.

Solving these equations, we find that x = 13 or x = 3.

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

There are two rational solutions.