Roots Calculator



ax2 + bx + c = 0

What is Roots Calculator

Roots calculator is a tool to calculate roots of any given quadratic equation, where we input value of coefficient a, b and c into the roots calculator.

Roots of a quadratic equation is basically the values of x for which quadratic equation ax2 + bx + c = 0 holds true.

These values of x for which quadratic equation ax2 + bx +c = 0 holds true are called the roots of a quadratic equation.

To calculate the roots of a quadratic equation, we apply the quadratic formula is, which is:

Roots(x1, x2) = −b ± √   b2 − 4ac 
         2a          

When we insert the value of a, b and c and solve the quadratic equation using the quadratic formula explained above, we get two values:

x1 = −b + √   b2 − 4ac 
         2a          

x2 = −b - √   b2 − 4ac 
         2a          

These two values of x – x1 and x2, which are calculated from the quadratic formula, also called roots of quadratic equation.

Hence, Roots Calculator calculates roots of a Quadratic equation

Nature of roots of Quadratic Equation

◾ If b2 – 4ac > 0, then √b2 − 4ac  is real; here roots calculator provides us an output of two real and distinct roots.

◾ If b2 – 4ac = 0, then √b2 − 4ac  is zero; here roots calculator provides us an output of only one real and equal root.

◾ If b2 – 4ac < 0, then √b2 − 4ac  is imaginary number; here roots calculator provides us an output of imaginary roots.

◾ If b2 – 4ac is a perfect square, then √b2 − 4ac  is a rational number; here roots calculator provides us an output of rational roots, else roots calculator provides us a solution of irrational roots.

How to use Roots calculator

Step 1 - Arrange the Quadratic Equation into Standard Form of Quadratic Equation, which is represented as ax2 + bx + c = 0

So, if we have to solve a quadratic equation

x2 - 7x = -12

First arrange this equation into the standard form ax2 + bx +c = 0. Hence,

x2 - 7x = -12 is now equal to x2 - 7x + 12= 0.

Now the quadratic equation has been successfully converted into standard form

Step 2 - Now, to use our Roots calculator, let's enter coefficient a, b and c in the calculator. So to find coefficient a, b and c, we compare our equation x2 - 7x + 12= 0 with ax2 + bx +c = 0.

Hence, we get

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

Step 3 - Insert the values of a, b and c in Quadratic formula:

Roots(x1, x2) = −b ± √   b2 − 4ac 
         2a          


x1 = −b + √   b2 − 4ac 
         2a          


=   −(-7) + √   (-7)2 − 4(1)(12)    = 4
         2(1)          


x2 = −b - √   b2 − 4ac 
         2a          


=   −(-7) - √   (-7)2 − 4(1)(12)    = 3
         2(1)          


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