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.