X^2-5x+9

To prepare for the university exams, let's look at the quadratic equation x^2 - 5x + 9.

First, let's determine if the equation can be factored. If it cannot be factored, we can then move on to solving the equation using the quadratic formula.

To factor the equation, we are looking for two numbers that multiply to 9 and add up to -5. However, since there are no two numbers that satisfy this condition, we can conclude that the equation cannot be factored.

Therefore, we will proceed to solve the equation using the quadratic formula. The quadratic formula is given as:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -5, and c = 9. Substituting these values into the quadratic formula, we have:

x = (-(-5) ± √((-5)^2 - 4(1)(9))) / (2(1))

Simplifying further:

x = (5 ± √(25 - 36)) / 2 x = (5 ± √(-11)) / 2

Since we have a negative value under the square root, it means that the equation has no real solutions. Therefore, the equation x^2 - 5x + 9 does not have any real roots.

In summary, the quadratic equation x^2 - 5x + 9 cannot be factored and does not have any real roots.