Quadratic Equation: Meaning, Formula and Real-time Examples

Quadratic Equation: A Quadratic Equation, also called Quadratics, is a polynomial equation of second degree. Simply put, it contains at least one term that is squared. In general, it can be represented as: ax² + bx + c = 0.

Here x is an unknown variable. a, b and c are numerical coefficients. Please note that a is not equal to 0. If a becomes zero, then, the equation results in bx + c=0. In such a case, it does not remain quadratic anymore. The values of x which satisfy the equation are called solutions.

Quadratic Equation: History and its Indian Connection

It is interesting to note that there was an algebraic formula contained in the Bakhshali manuscript that was written in India in the 7th century AD. This formula was used to solve quadratic equation.

It is further interesting to note that, in relation to Quadratic Equation, another person by name Muhammad, who was reportedly inspired by Brahmagupta, designed formulas to solve such equations.

Also Read: More on Quadratic Equation

Examples:

Here are a few examples of Quadratic Equation

6x² + 11x – 35 = 0
-4x² – 7x +12 = 0
5x² – 2x – 9 = 0

In all these examples, please note that a cannot be zero.

Real-time Examples

Though the Quadratic Equation seems complex, it has significance in our daily lives. For example, by solving quadratic equation, one can easily locate the position of a stone or a missile or an arrow as it travels in the air and falls back to earth

Furthermore, it can also be used in calculating distances travelled by cruises. A student may be surprised to know that a quadratic equation is a must for studying curved mirrors and lenses as well.

Terms To Know

Roots: The values of variables satisfying the given equation are called its roots.

Discriminant: b²-4ac is called the discriminant for the equation. It is important because it gives us an idea whether there are two solutions, one solution, or no solutions.

How To Solve A Quadratic Equation

Factoring Method: If ax² + bx + c = 0, a≠0 can be factorised into a product of two linear factors, then the roots of the quadratic equation ax² + bx + c = 0 can be found by equating each factor to zero.

Completing the Square Method: A quadratic equation can also be solved by the method of completing the square.

Apart from these two methods, it can also be solved by Formula Method and graphically as well.

Also Read: Different methods of solving quadratic equation

Take Help From Embibe To Understand Concepts Better

Embibe app is not just an app but a personalised teacher when it comes to helping students perform better. The app has 3D videos that a student can watch in order to understand concepts better, and also to know how they can be used in our daily life.

To get a better hold of the concept, a student can also learn more on concepts related to the subject on our Practice module and take up mock tests to prepare themselves better.

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