Quadratic functions how many solutions

Such solutions are known as zeros. Quadratic functions can be expressed in many different forms. The form written above is called standard form. The quadratic formula is one tool that can be used to find the roots of a quadratic equation. It is written:. The quadratic formula can always be used to find the roots of a quadratic equation, regardless of whether the roots are real or complex, whole numbers or fractions, and so on.

You can see why the second condition must be true by looking at the quadratic formula. Suppose we want to find the roots of the following quadratic function:. First, we need to set the function equal to zero, as the roots are where the function equals zero. Second, we need to identify the constants in the equation.

We can now substitute these values into the quadratic equation and simplify:. As I said, we cannot take the square root of a negative number, so if b 2 - 4 ac is negative, we have an error, and no solutions. It's beyond the scope of a GCSE course, so if you're confused by anything after this, don't worry! First of all though, I'll explain why nobody has told you this yet. So no whole number solutions exist. The same idea applies to the problem here.

We only have Real numbers that is, fractions, decimals, whole numbers and "irrational" numbers such as pi to deal with the question, and if you are asked to take the square root of a negative number, there are no Real solutions!

A solution does exist in the "Imaginary" numbers. Here's how the discriminant works. The discriminant isn't magic. It just shows how important that radical is in the quadratic formula. If its radicand is 0, for example, then you'll get. If, however, b 2 - 4 ac is negative, then you'll have a negative inside a square root sign in the quadratic formula, meaning only imaginary solutions.

Because the discriminant is negative, the quadratic equation has no real number solutions, only two imaginary ones. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. On the number of possible solutions for a quadratic equation. Ask Question. Asked 9 years, 2 months ago. Active 9 years, 2 months ago. Viewed 6k times. Red Banana. Red Banana Red Banana 22k 17 17 gold badges 78 78 silver badges bronze badges.

You aren't choosing them: by the time you're applying this formula you should know what they are. You get two for the price of one. Show 5 more comments.