To find out more about why you should hire a math tutor, just click on the "Read More" button at the right! When working with quadratic equations, we often see one or two real solutions. However, it is also possible that a quadratic will have no real solution. So, when does a quadratic have no solution?

We have seen two outcomes for solutions to quadratic equations, either there was one or two real number solutions. We have also learned that it is possible to take the square root of a negative number by using imaginary numbers. Having this new knowledge allows us to explore one more possible outcome when we solve quadratic equations. Consider this equation:. Using the Quadratic Formula to solve this equation, we first identify a, b, and c. We can place a, b and c into the quadratic formula and simplify to get the following result:.

We have seen two outcomes for solutions to quadratic equations; either there was one or two real number solutions. We have also learned that it is possible to take the square root of a negative number by using imaginary numbers. Having this new knowledge allows us to explore one more possible outcome when we solve quadratic equations.

Click to see full answer Regarding this, what does the discriminant tell you? The discriminant tells us the following information about a quadratic equation: If the solution is a real number or an imaginary number. If the solution is rational or if it is irrational.

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