Question

A quadratic equation is shown below:

9x2 − 16x + 60 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work

Answer 1

The radicand of a quadratic is b^2-4ac.

If it is greater than zero, there are two real solutions

If it is equal to zero, there is one real solution

If it is less than zero, there are no real solutions (though there are two imaginary solutions)

In this case the discriminant is 256-2160 so it is less than zero.

Therefore there are no real solutions, though there are two imaginary solutions, specifically (16±i√-1904)/18