Solution of Quadratic Equations
To find the solution set of a quadratic equation, following methods are used:
- factorization
- completing square
- use of quadratic formula
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Quadratic Equations
An equation of 2nd degree is called quadratic equation. In more detail, the quadratic equation is an equation, which contains the square of the unknown (variable) quantity, but no higher power. General or standard form of a quadratic equation: A 2nd degree equation in one variable x of the form as below, where a ≠ 0…
Subset
Set A is said to be a subset of a set B, if and only if each element of A is an element of B. It is denoted by A ⊆ B Super Set If a set A is a subset of set B then set B is a super set of set A. It…
Sets
A set is a collection of well defined distinct objects or symbols. Well defined objects mean that the objects possess a property that enables one to determine whether a given object is in the collection or not. For example, a set cannot consist of elements like moral values, concepts, evils or virtues. Element of a…
Chinese New Year
Chinese New Year is a holiday that celebrates the beginning of a new year according to the according to the Chinese lunar calendar. It is considered to be one of the most important holidays for Chinese families. The holiday is celebrated with big family gatherings, gift giving, the eating of symbolic foods and display and…
Solution of Quadratic Equation by Completing Square
To solve a quadratic equation by the method of completing square is illustrated through the following examples. Example Solve the equation x2 − 3x − 4 = 0 by completing square. Solution: x2 − 3x − 4 = 0 (i) Shifting constant term −4 to the right, we have x2 − 3x = 4 …
Exercise 1.1 (Math 10)
Question 1. Write the following quadratic equations in the standard form and point out pure quadratic equations. $ \pmb{ (i). \;\;\;\;\; (x + 7) (x − 3) = -7} $ Solution: The given quadratic equation is $$ (x + 7) (x − 3) = -7 \;\;\;\;\; (i) $$ Multiplying the expressions $ (x + 7)…
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