(50 points) The discriminant of a quadratic equation is equal to 30. How many solutions will it have? No solutions. One solution. Two solutions. Infinitely many solutions

A quadratic equation will have two solutions if its discriminant is equal to 30. The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 - 4ac. If the discriminant is positive, the quadratic equation will have two distinct real solutions.

Extra: The discriminant is very useful because it can tell us the nature and quantity of solutions without actually solving the equation. Here is a quick guide to the discriminant (D = b^2 - 4ac):

- If D > 0, the quadratic equation has two distinct real solutions. - If D = 0, the quadratic equation has exactly one unique solution (in other words, the graph of the equation touches the x-axis at exactly one point). - If D < 0, the quadratic equation has no real solutions but two complex solutions.

In our case, since the discriminant is 30, which is greater than zero, the quadratic equation will have two distinct real solutions. These solutions represent the points where the parabola, which is the graph of the quadratic equation, crosses the x-axis.