What is Quadratic Formula used for?

The quadratic function formula is the most used formula in algebra it is used for solving quadratic equations and finding their roots instantly without performing various steps. It gives the solution of the quadratic equations where the normal solution is not possible. We use this formula for solving various types of problems in algebra, factoring equations, graphing various curves, and others.

How to Solve Quadratic Equation Using Quadratic Formula?

Follow the steps given below to solve Using Quadratic Formula

Step 1: Write the given equation in standard form as, ax²+ bx + c = 0

Step 2: Carefully note the coefficient from the above equation as, a, b and c.

Step 3: Use the Quadratic Formula, x = [-b ± √(b² – 4ac)] / 2a

Step 4: Put all the values of a, b and c and simplify for x.

We can understand this with the help of the following example.

Example: Simplify x² + x – 6

Solution:

Step 1: Comparing x² + x – 6 with ax²+ bx + c = 0

Step 2: a = 1, b = 1, and c = -6

Step 3: Using the quadratic formula,

x = [-b ± √(b² – 4ac)] / 2a

Step 4: Simplifying

x = [-b ± √(b² – 4ac)] / 2a

⇒ x = [-1 ± √(1² – 4(1)(-6))] / 2(1)

⇒ x = [-1 ± √(4 + 4(1)(6))] / 2(1)

⇒ x = (-1 ± 5)/2

⇒ x = (-1-5)/2 = -3

⇒ x = (-1+5)/2 = 2

Thus, the values of x are x = -3 and x = 2

Read More,

• Quadratic Function
• Quadratic Inequalities
• Solving Cubic Equations

Quadratic Formula is used to find the roots (solutions) of any quadratic equation. Using the Quadratic formula real and imaginary all the types of roots of the quadratic equations are found.

The quadratic formula was formulated by a famous Indian mathematician Shreedhara Acharya, hence it is also called Shreedhara Acharya’s Formula. It is used to find the solution of the quadratic equation of the form ax² + bx + c = 0. So, let’s start learning about the concept of Quadratic Formula.