When can we have a no real solution of a quadratic equation?
A quadratic equation has no solution when the discriminant is negative. From an algebra standpoint, this means b2 < 4ac. Visually, this means the graph of the quadratic (a parabola) will never touch the x axis. Of course, a quadratic that has no real solution will still have complex solutions.
Why does a quadratic equation have two solutions?
There are usually two solutions because quadratic equations form a parabola in Cartesian coordinates. In almost any case involving a function, the parabola will intercept the x-axis at two points. Those two points are the two x values that cause the function to be equal to zero.
What does it mean if the discriminant is greater than 0?
When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots. In this case, we have two real roots.
What does that mean if the does not cross the X axis in a quadratic equation?
parabola
If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.
How do you tell if a quadratic equation has one two or no solution?
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.
What does it mean when an equation does not have a real solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.
Does every quadratic equation have 2 solutions?
Every quadratic equation has two solutions and can be factorized, but as level of difficulty rises, splitting may not be easy and one may tend to use quadratic formula.
How many solutions does the discriminant have greater than 0?
If the discriminant is greater than zero, there are two solutions. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.
What is the value of the discriminant of the quadratic equation − 1 5×2 − 2x?
What is the value of the discriminant of the quadratic equation -1=5×2-2x , and what does its value mean about the number of real number solutions the equation has? The discriminant is equal to −16, which means the equation has no real number solutions.
How do you know if a quadratic equation has one two or three roots?
If the discriminant is a positive number, there are two real-number solutions (the roots). The graph of the parabola intersects the x-axis at two points. If it is zero, there are still two roots but they are the same number: a “repeated root”.