![]() When a, b and c are real numbers, a ≠ 0 and discriminant is positive but not a perfect square then the roots of the quadratic equation ax 2 bx c = 0 are real, irrational and unequal. When a, b and c are real numbers, a ≠ 0 and discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax 2 bx c = 0 are real, rational unequal.Ĭase V: b 2 – 4ac > 0 and not perfect square When a, b and c are real numbers, a ≠ 0 and discriminant is zero (i.e., b 2 – 4ac = 0), then the roots α and β of the quadratic equation ax 2 bx c = 0 are real and equal.Ĭase III: b 2 – 4ac 0 and perfect square When a, b and c are real numbers, a ≠ 0 and discriminant is positive (i.e., b 2 – 4ac > 0), then the roots α and β of the quadratic equation ax 2 bx c = 0 are real and unequal. Generally, we denote discriminant of the quadratic equation by ‘∆ ‘ or ‘D’.ĭepending on the discriminant we shall discuss the following cases about the nature of roots α and β of the quadratic equation ax 2 bx c = 0. Thus the expression (b 2 – 4ac) is called the discriminant of the quadratic equation ax 2 bx c = 0. Then, the nature of the roots α and β of equation ax 2 bx c = 0 depends on the quantity or expression i.e., (b 2 – 4ac) under the square root sign. We know that α and β are the roots of the general form of the quadratic equation ax 2 bx c = 0 (a ≠ 0) ………………. Nature of the Roots of a Quadratic Equation If f(x) is a quadratic polynomial, then f(x) = 0 is called a quadratic equation.Īn equation in one unknown quantity in the form ax 2 bx c = 0 is called quadratic equation.Ī quadratic equation is an equation of the second degree. Using the quadratic formula is often the most convenient way. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. In elementary algebra, the quadratic formula is the solution of the quadratic equation. If you choose to write your mathematical statements, here is a list of acceptable math symbols and operators.A polynomial of the second degree is generally called a quadratic polynomial. The calculator will show you all the steps together with the reasoning or explanation behind each of the steps. Once you have the right expression or equation, Hit the calculate button to get started. Note you should only use the allowed notations and characters in order to obtain correct solution. ![]() To use this calculator, Insert your math expression on the textarea provided. Whether the roots are real or complex, the calculator is able show a step by step solution. Furthermore, the calculator can be used to find roots of varied problems. The online roots calculator is simple to use. How the Quadratic formula root calculator works X = \dfrac Need to learn Algebra through examples?įind more quadratic formula calculator Solved Examples Here: The calculator uses the quadratic formula to find the roots of a quadratic equation. First, find the roots or solutions your way, and then use the roots calculator to confirm your answer. With our online calculator, you can learn how to find the roots of quadratics step by step. Learning math with examples is the best approach. An equation root calculator that shows steps A quadratic equation has two roots or zeroes namely Root1 and Root2. ![]() Hit the calculate button to get the roots. To solve an equation using the online calculator, simply enter the math problem in the text area provided. A quadratic is a second degree polynomial of the form: ax^2 bx c=0 where a\neq 0. This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation.
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