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Q: The determines how many solutions a quadratic equation will have and whether they are real or imaginary?

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That's true. Complex and pure-imaginary solutions come in 'conjugate' pairs.

The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.

When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.

If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.

0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.

A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.

The quadratic has no real solutions.

It is a quadratic equation that normally has two solutions

A quadratic equation normally has 2 solutions and can be solved by using the quadratic equation formula.

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