Can the discriminant of a quadratic equation be zero?
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
What happens if the discriminant is 0?
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, there is exactly one real root. This value of x is the one distinct real root of the given equation.
Which quadratic equation has a discriminant of 0?
If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1. D > 0 means two real, distinct roots.
Can a quadratic function ever be even?
Strictly-speaking, a quadratic function always has two roots, but they might not be real numbers. The function f(x)=x2 is called an even function because f(−x)=f(x); for example, f(−2)=f(2)=4.
How many zeros are there if the discriminant is 0?
When the discriminant equals 0, there will be only one zero, and when it’s negative, there will be no zeros. Let’s plug the A,B, and C values from our example functions into the discriminant to compare the results.
How many solutions does a quadratic have if the discriminant is 0?
one solution
The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.
What is discriminant in quadratic equation?
The discriminant of the Quadratic Formula is the quantity under the radical, b2−4ac b 2 − 4 a c . It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0 , there is 1 real repeated solution.
How many solutions does the discriminant of 0 have?
two solutions
It tells you the number of solutions to a quadratic equation. 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.
When discriminant is zero then roots are?
real and equal
Clearly, the discriminant of the given quadratic equation is zero. Therefore, the roots are real and equal.
Is a quadratic equation even or odd?
You may be asked to “determine algebraically” whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.
Why does a parabola never go below zero?
In the graph, the highest or lowest point of a parabola is the vertex. The vertex of the graph of y=x2 is (0,0). Again, a large negative value of a makes the parabola narrow; a value close to zero makes it wide. For an equation in standard form, the value of c gives the y-intercept of the graph.
What is the zero of a quadratic function?
The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.
How do you find the discriminant of an equation?
Full Answer. To find the discriminant, evaluate the formula with the coefficient values substituted. In the example from Step 2, 3^2-4*4*1 = 9-16 = -7. The discriminant is -7. A negative discriminant tells you the quadratic equation has two complex solutions. A positive discriminant indicates two real solutions. A discriminant of 0 indicates one real solution.
What is the discriminant and what does it mean?
A discriminant is a value calculated from a quadratic equation. It use it to ‘discriminate’ between the roots (or solutions) of a quadratic equation. If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots.
How do you find 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!
Can a quadratic equation have only one real solution?
The first way to tell if a quadratic has one solution is to look at the discriminant. If the discriminant is zero , then the quadratic equation has only one real solution. Remember that for the quadratic equation ax 2 + bx + c = 0, the discriminant is the expression b2 – 4ac.