#### How can you tell when a quadratic equation has no real solutions?

## What does it mean if an equation has no real solutions?

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. This is because there is truly no solution—there are no values for x that will make the equation 12 + 2x – 8 = 7x + 5 – 5x true.

## Do quadratic equations have real solutions?

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.

## How do you know if a graph has no real solutions?

No x-intercept means that it does not cross the x-axis. Thus two solutions is definitely ruled out. However, if you DO NOT INCLUDE a point of coincidence (Vertex coincides with the x-axis) in the phrase “does not have an x-intercept”. Then there could be a single value solution if you equate the quadratic to 0.

## Which equations have no real solutions?

If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.

## Is 0 0 infinite or no solution?

For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions. For an answer to have no solution both answers would not equal each other.

## Why are there two solutions in quadratic equations?

A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.

## What is the solution to a quadratic equation?

The “solutions” to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph). Just plug in the values of a, b and c, and do the calculations. We will look at this method in more detail now.

## Do all quadratic equations have two solutions?

A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.

## What is the symbol for no solution?

We need a way to denote the fact that there are no solutions here. In solution set notation we say that the solution set is empty and denote it with the symbol : ∅ . This symbol is often called the empty set.

## What is a repeated real solution?

When the left side factors into two linear equations with the same solution, the quadratic equation is said to have a repeated solution. We also call this solution a root of multiplicity 2, or a double root.

## How do you know if an equation has two solutions?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.

## Is 0 a real number?

Real numbers consist of zero (0), the positive and negative integers (-3, -1, 2, 4), and all the fractional and decimal values in between (0.4, 3.1415927, 1/2). Real numbers are divided into rational and irrational numbers.