SOLUTION:
We are to select the quadratic equation that has no real solution.
Facts about Quadratic equations;
When considering,
[tex]b^2\text{ - 4ac}[/tex]If you get a positive number, the quadratic will have two unique solutions. If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
Looking at all the four options, I have examined all and the only one found to be negative is the second option. Let's consider it together
a = 9, b = -25 and c = 30
(b x b ) - 4 x a x c
(-25 x -25) - 4 (9) (30)
625 - 1080
- 455
-455 < 0
Since the discriminant is less than this quadratic equation is expected to have no real solution.
You can as well try the other three options one is zero and the remaining two are greater than zero.