If the discriminant is positive, then the function has two real zeros. If it is zero, then the function has one real zero. If it is negative, then it has two complex conjugate zeros.
This assumes that we are talking about a standard second order polynomial equation, i.e. quadratic equation, in the form Ax2 + Bx + C = 0, and that the discriminant is B2 - 4AC, which is a part of the standard solution of these kind of equations.
To find the discriminant of a quadratic function, first express it in descending powers, thusax^2 + bx + c = 0 where a, b and c are real and a is non-zero.Then the discriminant is b^2 - 4ac
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
The number of function is Geometry
Whether or not that there is a solution to a quadratic equation,
To find the discriminant of a quadratic function, first express it in descending powers, thusax^2 + bx + c = 0 where a, b and c are real and a is non-zero.Then the discriminant is b^2 - 4ac
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
The discriminant is 49.
In general, there is no simple method.
by synthetic division and quadratic equation
If the discriminant is negative, there are 0 interceptsIf the discriminant is zero, there is 1 interceptIf the discriminant is positive, there are 2 intercepts
The zeros of a function are the values of the independent variable where the dependent variable has value of zero. In a typical representation where y = f(x), the zeroes are the points x where y is 0.
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
You could try setting the function equal to zero, and finding all the solutions of the equation. Just a suggestion.
answer is:Find the function's zeros and vertical asymptotes, and plot them on a number line.Choose test numbers to the left and right of each of these places, and find the value of the function at each test number.Use test numbers to find where the function is positive and where it is negative.Sketch the function's graph, plotting additional points as guides as needed.
The number of function is Geometry