Discriminant Calculator

Discover the nature of quadratic equation roots with our Discriminant Calculator, revealing real, repeated, or complex solutions effortlessly.

Updated at:May 23, 2024

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable (x)(x), with the form ax2+bx+c=0ax^2 + bx + c = 0, where a0a \neq 0

What is the discriminant?

The discriminant of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is given by:

D=b24acD = b^2 - 4ac

It provides important information about the nature of the roots of the equation.

How does the discriminant determine the nature of the roots?

The discriminant helps in determining the nature of the roots of a quadratic equation:

  • If D>0D > 0, there are two distinct real roots.
  • If D=0D = 0, there is one real root (a repeated root).
  • If D<0D < 0, there are no real roots; instead, there are two complex roots.
Can the calculator handle complex roots?

Yes, the calculator can identify if a quadratic equation has complex roots based on the discriminant. However, it does not provide the complex roots themselves.

What is a discriminant calculator and how does it work?

A discriminant calculator is an online mathematical tool that helps you solve the discriminant of quadratic equations, and provides you with the nature of the roots. It also gives you the complete discriminant solution with the full process using the discriminant formula. It takes the values of the coefficients of a, b, and c and calculates them using the discriminant formula. D=b24acD = b^2 - 4ac

How can a discriminant calculator help in solving quadratic equations?

A discriminant calculator is very helpful for finding the discriminant value of a quadratic equation without knowing its formula or value calculation, and it also provides the full solution with the formula.

Can a discriminant calculator be used to determine the nature of the roots of a quadratic equation?

Yes, a discriminant calculator can be used to determine the nature of the roots of a quadratic equation based on the value of the discriminant.

How accurate are the results obtained from a discriminant calculator?

The accuracy of a discriminant calculator is 100% because it uses an algorithm based on the discriminant formula, which cannot be wrong. It has the ability to find both larger and smaller discriminant values.

What input values are required for the calculator?

The calculator requires three inputs:

  • (a)(a): The coefficient of x2x^2 (must be non-zero)
  • (b)(b): The coefficient of xx
  • (c)(c): The constant term

Ensure that the input values for (a)(a), (b)(b), and (c)(c) are valid numbers. For example, enter the coefficients as numerical values without any additional characters or spaces.