![]() ![]() 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. 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: $$D=(-6)^2 - 4\cdot2\cdot3=36-24=12 $$ 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. 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. If you want to learn more about if.else statements, go to JavaScript if.else Statement.During your algebra exploration, you'll inevitably encounter quadratic equations. The above program uses an if.else statements. This rounds up the decimal number to two decimal values. You can see that toFixed(2) is also used in the program. In the above program, the Math.sqrt() method is used to find the square root of a number. In the above output, the discriminant will be less than 0 and the corresponding code is executed. The roots of quadratic equation are 1.50 + 2.78i and 1.50 - 2.78i Here, the discriminant will be equal to 0 and the corresponding code is executed. The above input values satisfy the else if condition. ![]() The roots of quadratic equation are 3 and 3 Here, the discriminant will be greater than 0 and the corresponding code is executed. The above input values satisfy the first if condition. The roots of quadratic equation are -1 and -5 Root2 = (-b - Math.sqrt(discriminant)) / (2 * a) Ĭonsole.log(`The roots of quadratic equation are $i` Root1 = (-b + Math.sqrt(discriminant)) / (2 * a) condition for real and different roots Let c = prompt("Enter the third number: ") Let b = prompt("Enter the second number: ") Let a = prompt("Enter the first number: ") Nature of the roots of quadratic equationsĮxample: Roots of a Quadratic Equation // program to solve quadratic equation If the discriminant is less than 0, the roots are complex and different.If the discriminant is equal to 0, the roots are real and equal.If the discriminant is greater than 0, the roots are real and different.The term b 2-4ac is known as the discriminant of a quadratic equation. To find the roots of such equation, we use the formula, (root1,root2) = (-b ± √b 2-4ac)/2 The standard form of a quadratic equation is: ax 2 + bx + c = 0, where This program computes roots of a quadratic equation when its coefficients are known. ![]()
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