3х^2-5х+10

The expression you provided is a quadratic equation. To prepare for university exams, let's discuss some essential mathematics concepts related to this equation.

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable.

In your equation, 3x^2 - 5x + 10, a = 3, b = -5, and c = 10.

Here are some important concepts related to quadratic equations:

1. Factoring: The first step to solve a quadratic equation is to check if it can be factored. Factorization can be done by finding two binomials whose product is equal to the given equation. However, it may not always be possible to factorize a quadratic equation in a simple manner.

2. Quadratic Formula: If factoring is not possible or feasible, you can use the quadratic formula to solve the equation. The quadratic formula is x = (-b ± √(b^2-4ac))/(2a). By substituting the values of a, b, and c in the formula, you can find the solutions for x.

3. Discriminant: The discriminant of a quadratic equation is the expression inside the square root in the quadratic formula, (b^2-4ac). The value of the discriminant determines the nature of the solutions. If the discriminant is positive, there are two distinct real solutions. If the discriminant is zero, there is one repeated real solution. If the discriminant is negative, there are no real solutions, and the solutions are complex.

Now, let's solve your equation using the quadratic formula:

a = 3, b = -5, c = 10

x = (-(-5) ± √((-5)^2-4(3)(10)))/(2(3)) = (5 ± √(25-120))/(6) = (5 ± √(-95))/(6)

Since the discriminant (-95) is negative, the solutions are complex.

Therefore, the solutions to the equation 3x^2 - 5x + 10 are:

x = (5 + i√95)/(6) and x = (5 - i√95)/(6).

Remember to double-check the calculations and refer to your textbook or lecturer's guidelines for any specific instructions or additional methods. Good luck with your preparation for your university exams!