In algebra, an algebraic equation (polynomial equation) is an equation which is of the form
A = B
Here, A and B are the polynomials with coefficients. In other words, an equation is of the form of a polynomial with a finite number of terms and it is equated to zero is known as algebraic equations. The expression in the equations may be either monomial, binomial, trinomial or polynomial. Let’s consider an equation
3x – 5 = 4
Here the equation is of the binomial form where 3 is the coefficient of x, x is a variable and 4 and 5 are the constants.
In order to convert into proper algebraic expressions, equate this expression to zero and it becomes,
3x – 5 – 4 = 0 (or) 3x – 9 = 0
If the algebraic equation is of the higher degree of 2 is known as a quadratic equationand is of the form ax2+ bx + c = 0. There are several methods to solve quadratic expressions. They are
- Factoring method
- Square root method
- Completing the square method
- Quadratic Formula method
Consider an equation x2 -4x – 12 = 0
In this method, the equation can be factorised into (x-6)(x+2) = 0
When you equate this to zero, it becomes
(x-6) = 0 or (x+2)=0
x=6 or x=-2
Square Root Method
The square root method is used when the term bx = 0
For example, x2 – 1 = 24
Here, the term bx = 0
To use this method, isolate the x2 term on the left side and add +1 on both the sides to eliminate the constant term and it becomes x2 = 25
Now, take square roots on both the sides, to find the value of x
Therefore, x = ± 5
This can be written as x = +5 or x = -5
Completing the Square Method
The procedure to solve the quadratic expression as follows
- Divide all the terms by “a” (coefficients of x2)
- Move the term c/a to the right side of the equation
- Now complete the square on the left side of the expression.
- To balance the expression, add the same number to the right side of the expression
- Take square root on both the sides
- Finally, to find the value of x, subtract or add the number that remains on the left side of the equation on both sides.
Quadratic Formula Method
Among all these methods, the quadratic formula method is the most appropriate method to solve the problems. When the quadratic algebraic equation is equated to zero, substitute the coefficient value like a, b, and c in the formula, to find the value of x.
The quadratic equation formula is given as
Likewise, there are different methods available to solve the problems from concepts like permutation and combination, trigonometry, probability, differentiation, integration. Subscribe to BYJU’S YouTube channel to learn distinct methods and also download BYJU’S – The Learning App to explore different maths-related articles.