The square root of -20 is not a real number! This quadratic equation has no real solutions. Note: This quadratic equation will have twocomplexsolutions involving imaginary numbers, but the focus is on real solutions here. Look at what the graph of a quadratic equation with no real solutions...
Look at what the graph of a quadratic equation with no real solutions looks like: What is the quadratic formula? The quadratic formula is x =-b +/- sqrt(b^2 - 4ac)/2a. It is a very important formula in mathematics which can be used to find the real (or complex) solutions to any...
The discriminant of the Quadratic Equation:The discriminant of the quadratic equation is used to find the nature of the roots. If the discriminant is positive, then the roots (zeros) of the quadratic equation will be real and distinct. The discriminant of the equatio...
Before about 1800, most mathematicians would have told you that the quadratic equation with negative discriminant has no solutions. Associated with this point of view, the square root of a negative number has acquired the designation “imaginary.” The sum of a real number with an imaginary is ...
Can I solve any polynomial with this calculator? No, this calculator specifically solves second-degree polynomials Higher-degree polynomials require different methods or tools. Why is understanding the discriminant important? The discriminant helps determine whether a quadratic equation has real or complex...
The quadratic equation has only one root when Δ = 0. The solution is equal tox = -B/2A. It is sometimes called a repeated or double root. The quadratic equation has no real solutions for Δ < 0. You can also graph the functiony = Ax² + Bx + C. Its shape is a parabola, ...
We may also treat this type of solution as unreal, stating that no real solutions exist for this equation, by writing DNE. We will study complex numbers more thoroughly in a later module.Using the Quadratic FormulaThe fourth method of solving a quadratic equation is by using the...
Write a quadratic equation in x with the following solutions Explain how to determine if a quadratic equation has no real solution. Solve the equation for real solutions, if there are any, by using the quadratic formula. 2x^2 = 9x + 1 If the solutions to a quadratic equation are 3 and...
Up to this point, we would have said that √−39−39 is not defined for real numbers and determine that this equation has no solutions. But, now that we have defined the square root of a negative number, we can also define a solution to this equation as follows....
Step 4Factor the completed square and combine the numbers on the right-hand side of the equation. Step 5Find the square root of each side of the equation. Step 6Solve for x and simplify. If step 5 is not possible, then the equation has no real solution. ...