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Quadratic Equation Calculator
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Quadratic equation is a polynomial equation which is in the form of Ax$^{2}$ + Bx + C = 0 (second degree). Quadratic Equation Calculator (or Quadratic Equation Solver) is an online tool to solve a quadratic equation. If any quadratic equation is given then it can find factors of that equation, i.e. for the equation of the form Ax$^{2}$ + Bx + C = 0, it will find the values of x.

This calculator solves the quadratic equation with negative discriminant also, i.e. this calculator can find out imaginary roots (or complex roots) also.

 

Steps to Solve the Quadratic Equation

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Step 1 :  

Observe the value of a, b and c from the quadratic equation.



Step 2 :  

Find the value of discriminant(D) by applying the formula D = b2 - 4ac.



Step 3 :  

If the value of discriminant is less than zero, write "roots does not exist/ imaginary. And if discriminant is greater or equal to zero, then find the roots of an equation by applying the formula x1= $\frac{-b + \sqrt{D}}{2a}$ and x2= $\frac{-b - \sqrt{D}}{2a}$



Examples on Quadratic Equation Calculator

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  1. Find the roots of an equation x2 + 7x + 12 = 0?


    Step 1 :  

    Here a = 1, b = 7, c = 12



    Step 2 :  

    D = b2 - 4ac = 72 - 4 × 1 × 12 = 49 - 48



    D = 1



    Step 3 :  

    x1 = $\frac{-b + \sqrt{D}}{2a}$ = $\frac{-7 + \sqrt{1}}{2 × 1}$ = $\frac{-6}{2}$ = -3


    x2 = $\frac{-b - \sqrt{D}}{2a}$ = $\frac{-7 - \sqrt{1}}{2 × 1}$ = $\frac{-8}{2}$ = -4



    Answer  :  

    x1 = -3

     

     

     

     

     

     

     

    x2 = -4



  2. Find the root of an equation x2 + 4x + 5 = 0?


    Step 1 :  

    Here a = 1, b = 4, c = 5



    Step 2 :  

    D = b2 - 4ac = 42 - 4 × 1 × 5 = 16 - 20



    D = -4



    Step 3 :  

    Roots are imaginary, since discriminant is less than zero.



    Answer  :  

    Roots are imaginary



More Quadratic Equation Calculator
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