Formula for Quadratic Equation

December 28, 2021

Basic Concepts of Quadratic Equations

A Quadratic Equation is the equation that can be rearranged in standard form ax² + bx + c = 0 as where x is a variable and a, b, and c represent constants , where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term. Let us have a look on some of the basic concepts and Formula for Quadratic Equation that will help you to memorize this topic easily and rapidly.

Formula for Quadratic Equation & Definitions

An equation where the highest exponent of the variable is a square. Standard form of quadratic equation is ax²+bx+c = 0
Where, x is the unknown variable and a, b, c are the numerical coefficients.

Quadratic Equations Formulas

If ax²+bx+c = 0 is a quadratic equation, then the value of x is given by the following formula
x = $\frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$

Formula of Quadratic Equation & Method of Quadratic Questions

Factorization

It is very simple method to to solve quadratic equations. Factorization give 2 linear equations
For example: x² + 3x – 4 = 0

Here, a = 1, b = 3 and c = -4

Now, find two numbers whose product is – 4 and sum is 3.

So, the numbers are 4 and -1.

Therefore, two factors will be 4 and -1

Completing the Square Method

Every Quadratic question has always a square term. If we could get two square terms of quality sign we can get a linear equations. Middle term is called as ‘b’ and splited by $(\frac{b}{2})^2$

For example : – x²+ 4x +4

Here x² =1, b= 4

$(\frac{b}{2})^2$ = $(\frac{4}{2})^2$ = 4

x²+4x+4 = -1+4

(x+2)² = 3

Take the square of both side

x+2 = ± $\sqrt{3}$ = ± 1.73

Therefore, x = -0.27 or -3.73

Formulas of Quadratic Equations & Key points to Remember

Other basic concepts to remember while solving quadratic equations are:

1.Nature of roots

- Nature of roots determine whether the given roots of the equation are real, imaginary, rational or irrational. The basic formula is b² – 4ac.
- This formula is also called discriminant or D. The nature of the roots depends on the value of D. Conditions to determine the nature of the roots are:
- If D < 0, than the given roots are imaginary.
- If D = 0, then roots given are real and equal.
- If D > 0, then roots are real and unequal.
- Also, in case of D > 0, if the equation is a perfect square than the given roots are rational, or else they are irrational.

2. Sum and product of the roots

- For any given equation the sum of the roots will always be $– \frac{b}{a}$ , and the product of the roots will be $– \frac{c}{a}$ . Thus, the standard quadratic equation can also be written as x² – (Α + Β)x + Α*Β = 0

3. Forming a quadratic equation

- The equation can be formed when the roots of the equation are given or the product and sum of the roots are given.

How to Solve Quadratic Equation Quickly

Some Questions on Quadratic Equations