Quadratic Equations Formulas
2026-02-28 10:31 Diff
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Last updated on September 25, 2025

In mathematics, quadratic equations are polynomial equations of degree 2. The general form of a quadratic equation is ax² + bx + c = 0. In this topic, we will learn the formulas related to solving quadratic equations, such as the quadratic formula and methods of factorization.

List of Quadratic Equations Formulas

Quadratic Formula

The quadratic formula is used to find the solutions of a quadratic equation ax² + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a)

Factorization Method

The factorization method involves expressing the quadratic equation in a product of linear factors. A quadratic equation ax² + bx + c = 0 can be factored as (px + q)(rx + s) = 0.

Solving these factors gives the roots of the equation.

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Completing the Square

Completing the square is another method to solve quadratic equations.

It involves rearranging the equation to form a perfect square trinomial.

The equation ax² + bx + c = 0 can be rewritten as (x + d)² = e, where d and e are constants derived from the coefficients a, b, and c.

Importance of Quadratic Equations Formulas

In mathematics and real-life applications, solving quadratic equations is essential. Here are some important uses of quadratic equations:

  • Quadratic equations help in determining the trajectory of objects in physics.
     
  • They are used in calculating areas and optimizing functions in calculus.
     
  • The quadratic formula provides a straightforward way to find roots without factorization.

Tips and Tricks to Memorize Quadratic Equations Formulas

Students may find quadratic formulas challenging, but with some tips, they can master these easily:

  • Remember the quadratic formula using the mnemonic: "Negative b, plus or minus the square root, of b squared minus 4ac, all over 2a."
     
  • Practice converting quadratic equations to different forms (standard, vertex, and factored) to get familiar with them.
     
  • Use flashcards to memorize the formulas and practice problems for reinforcement.

Common Mistakes and How to Avoid Them While Using Quadratic Equations Formulas

Students often make errors when solving quadratic equations. Here are some common mistakes and ways to avoid them:

Problem 1

Solve the quadratic equation 2x² - 8x + 6 = 0 using the quadratic formula.

Okay, lets begin

The solutions are x = 3 and x = 1.

Explanation

For the equation 2x² - 8x + 6 = 0, a = 2, b = -8, c = 6.

Using the quadratic formula: x = (-(-8) ± √((-8)² - 4*2*6)) / (2*2) x = (8 ± √(64 - 48)) / 4 x = (8 ± √16) / 4 x = (8 ± 4) / 4

The solutions are x = 3 and x = 1.

Well explained 👍

Problem 2

Solve the quadratic equation x² + 6x + 9 = 0 by factorization.

Okay, lets begin

The solution is x = -3.

Explanation

Factorize the equation x² + 6x + 9 = 0: (x + 3)(x + 3) = 0

The solution is x = -3.

Well explained 👍

Problem 3

Solve the quadratic equation x² - 4x - 5 = 0 by completing the square.

Okay, lets begin

The solutions are x = 5 and x = -1.

Explanation

Rearrange x² - 4x - 5 = 0: x² - 4x = 5

Complete the square: (x - 2)² = 9 x - 2 = ±3

The solutions are x = 5 and x = -1.

Well explained 👍

FAQs on Quadratic Equations Formulas

1.What is the quadratic formula?

The quadratic formula is used to find the roots of a quadratic equation ax² + bx + c = 0: x = (-b ± √(b² - 4ac)) / (2a)

2.What is the factorization method?

The factorization method involves expressing the quadratic equation as a product of linear factors and solving for the roots.

3.How do you complete the square?

To complete the square, rearrange the quadratic equation to form a perfect square trinomial, then solve it for the variable.

4.Why do quadratic equations have two solutions?

Quadratic equations have two solutions because they are based on the square of the variable, which can have both positive and negative roots.

5.What happens if the discriminant is negative?

If the discriminant (b² - 4ac) is negative, the quadratic equation has complex or non-real solutions.

Glossary for Quadratic Equations Formulas

  • Quadratic Equation: A polynomial equation of degree 2, typically in the form ax² + bx + c = 0.
  • Discriminant: The expression b² - 4ac in the quadratic formula, determining the nature of the roots.
  • Roots: The solutions of the quadratic equation, where the graph intersects the x-axis.
  • Completing the Square: A method used to solve quadratic equations by forming a perfect square trinomial.
  • Factorization: Expressing a quadratic equation as a product of linear factors to find the roots.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.