How many solutions does the discriminant have?
If the discriminant is equal to 0, the quadratic equation has 1 real solution. If the discriminant is less than 0, the quadratic equation has 0 real solutions. (Instead of real solutions, the quadratic equation has 2 imaginary solutions.)
How many solutions are there if the discriminant is 4?
Nature of the Solutions
| Value of the discriminant | Type and number of Solutions |
|---|---|
| Example :y=3×2+4x−4Discriminant42−4⋅3⋅−4=64 | If the discriminant is positive and also a perfect square like 64, then there are 2 real rational solutions. |
How many solutions are there?
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
How many solutions would a quadratic with a discriminant of 109 have?
The value of the discriminant is 109 and the equation has two irrational solutions and is best solved with the quadratic formula. The discriminant is a perfect square so there will be two rational solutions and the equation can be solved by factoring.
How do you find solutions?
Determine whether a number is a solution to an equation.
- Substitute the number for the variable in the equation.
- Simplify the expressions on both sides of the equation.
- Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
What is discriminant formula?
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
How many solutions based on discriminant?
If the discriminant is a positive number, then there are 2 real solutions. This means that the graph of the parabola interepts the x-axis at 2 distinct points . If the discriminant is positive and also a perfect square like 64, then there are 2 real rational solutions.
How do you use the discriminant?
In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation. The expression used to find the discriminant is the expression located under the radical in the quadratic formula! In this tutorial, get introduced to the discriminant of a quadratic equation!
What does the discriminant tell you?
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
How do you find the discriminant of a quadratic equation?
The discriminant in a quadratic equation is found by the following formula and the discriminant provides critical information regarding the nature of the roots/solutions of any quadratic equation. discriminant= b² − 4ac. Example of the discriminant. Quadratic equation = y = 3x² + 9x + 5.
