Quadratic Equation Calculator

This quadratic equation calculator calculates the real and imaginary roots using the standard formula and shows the working of the main steps. Once you have an equation in the standard form ax² + bx + c = 0, you simply enter the coefficients a, b, and c together with their positive or negative signs and the calculator will do the rest for you.



+/- a:


+/- b:


+/- c:


Discriminant D:


Root 1:


Root 2



The Discriminant

First, calculate the discriminant part b² - 4 × a × c. This is the part under the square root sign. If a, or c coefficients are negative then do not forget that a negative number multiplied by another negative makes a positive. Also, do not forget the -4, as students usually trip up here.

Real / Imaginary Roots

The next step involves taking the square root of the discriminant. If it is negative then your calculator will not be able to give you the square root of a negative number. You will therefore have to take the square root of the positive number and place an "i" in front of it to signify that it is an imaginary number.

Use this figure for the rest of the formula. By calculating in logical steps, you will get more information about your equation and it simplifies a little as well.

Instructions

This root calculator provides the solutions to real and imaginary roots. This might be useful for teachers as a generator to make some sample questions for the classroom activity and test.

Just enter the coefficients a, b, and c, together with their sign, whether + or - and then press the calculate button.

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