What is Discriminant Calculator

The discriminant calculator is an online calculator tool, which calculates the discriminant of a given quadratic equation.

For a quadratic equation ax^{2} + bx + c = 0, where a ≠ 0, the formula of discriminant is b^{2} – 4ac.

Discriminant is also denoted by symbol Δ

∴ Δ = b^{2} – 4ac

The value of discriminant helps in deciphering

◾ **Number of roots** – whether the quadratic equation has two roots, one root or none.

◾ **Type of roots** - whether the roots are real and imaginary.

Nature of roots of Quadratic Equation

◾ If Δ > 0, then √Δ is real; hence we get two real and distinct roots.

◾ If Δ = 0, then √Δ is also zero; hence values of both x_{1} and x_{2} would be same and hence we get real and equal roots.

◾ If Δ < 0, then √Δ is imaginary number; hence we get imaginary roots.

◾ If Δ is a perfect square, then √Δ is a rational number; hence we get rational roots, else we get irrational roots.

To summarise

Value of discriminant | Number of roots | Type of roots |
---|---|---|

Δ > 0 | 2 | Real |

Δ = 0 | 1 | Real |

Δ < 0 | 0 | Imaginary |

How to use Discriminant calculator

**Step 1** - To use Discriminant Calculator, the first step is to convert the quadratic equation where we want to use Discriminant calculator, into Standard Form of Quadratic Equation.

The Standard form of quadratic equation is ax^{2} + bx + c = 0

Hence, the first step is to change our quadratic equation in the standard form which is represented as ax^{2} + bx +c = 0

So, Let's suppose we have to solve a quadratic equation which is currently in the form of

x^{2} - 10x = -16

So we rearrange this equation, so that is represented in the standard form ax^{2} + bx +c = 0. Hence,

x^{2} - 10x = -16 is now equal to x^{2} - 10x + 16= 0.

Now the quadratic equation has been successfully converted into standard form

**Step 2** - Now, this is the most important step, where find value of coefficient a, b and c by comparing it with Standard Form of Quadratic Equation ax^{2} + bx +c = 0.

For example, comparing x^{2} - 10x + 16= 0. with ax^{2} + bx +c = 0, we get

a = 1,

b = -10,

c = 16

**Step 3** - Insert the values of a, b and c in formula of discriminant calculator b2 – 4ac

Hence, Discriminant, Δ = (-10)^{2} – 4(1)(16) = 36

Since Δ > 0, hence the equation has two real and distinct roots

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