Final answer:
The discriminant of the quadratic equation x^2 - 7x +16 = 0 is -15, indicating that there are 0 real solutions and 2 imaginary solutions to the equation.
Step-by-step explanation:
To determine how many real solutions the quadratic equation x^2 - 7x +16 = 0 has, we need to use the discriminant, which is the part of the quadratic formula under the square root: b^2 - 4ac. In this case, a=1, b=-7, and c=16. Calculating the discriminant gives us (-7)^2 - 4(1)(16) which simplifies to 49 - 64, or -15. Because the discriminant is negative, this equation has 0 real solutions and instead has 2 imaginary solutions.