This means the parabola does not intersect the x-axis at all. Instead, it has two complex roots (solutions). When the discriminant is negative, the quadratic equation has no real roots. Negative Discriminant $$$\left(D\lt0\right) $$$ For example, in the equation $$$x^2-6x+9=0 $$$, the discriminant is $$$0 $$$, so there is one real solution (or two identical real solutions), namely, $$$x=3 $$$. In other words, the parabola touches the x-axis at exactly one point.
![solving quadratic equations calculator solving quadratic equations calculator](https://i.ytimg.com/vi/GMz0xafliN4/maxresdefault.jpg)
When the discriminant is zero, the quadratic equation has exactly one real root or two real roots that are the same (also known as repeated roots). Zero Discriminant $$$\left(D=0\right) $$$ For example, in the equation $$$x^2-5x+6=0 $$$, the discriminant is $$$1 $$$ (a positive number), so there are two real and distinct solutions, namely, $$$x=2 $$$ and $$$x=3 $$$. This means the parabola represented by the equation crosses the x-axis at two distinct points. The quadratic equation has two distinct real roots when the discriminant is positive. Positive Discriminant $$$\left(D\gt0\right) $$$ In the context of a quadratic equation, the discriminant, represented by the formula $$$D=b^2-4ac $$$, carries crucial information about the nature of the roots (solutions) of the equation. What Does a Positive and Negative Discriminant Represent? Since $$$D\gt0 $$$, this equation has two distinct real roots. Substituting these values into the discriminant formula gives: $$D=(-6)^2 - 4\cdot2\cdot3=36-24=12 $$
![solving quadratic equations calculator solving quadratic equations calculator](https://i.ytimg.com/vi/_Rg0Yg2M2tE/maxresdefault.jpg)
Consider the quadratic equation $$$2x^2-6x+3=0 $$$. The discriminant $$$D $$$ of this equation is given by the formula: $$D=b^2-4ac $$ The general form of a quadratic equation is: $$ax^2+bx+c=0, $$ A quadratic equation is a second-order polynomial equation in a single variable $$$x $$$, with a non-zero coefficient for $$$x^2 $$$. In algebra, the discriminant plays a crucial role in determining the nature of the roots of a quadratic equation.
![solving quadratic equations calculator solving quadratic equations calculator](https://media.kunduz.com/media/sug-question-candidate/20240221235540850978-6624282.jpg)
The calculator will calculate the discriminant.Īfter the calculation, the Discriminant Calculator will display the discriminant value instantly on the screen. Once you've entered the coefficients, click on the "Calculate" button. Make sure you enter it correctly to get accurate results. Input your quadratic equation in the designated field. By computing the discriminant, you gain insights into the character of the roots of the quadratic equation. Our Discriminant Calculator is an efficient and potent tool to assist you in effortlessly calculating the discriminant. During your algebra exploration, you'll inevitably encounter quadratic equations.