Equations
Equations
In the context of Quantitative Ability, equations refer to mathematical expressions that equate two quantities or values. Solving equations involves finding the values of the variables that satisfy the given equation. Equations are an essential part of various mathematical problems and real-life scenarios.
There are different types of equations encountered in Quantitative Ability, including:
Linear Equations:
An equation in which the highest power of the variable is 1 is known as linear equation.
The general form of a linear equation in one variable 'x' is: ax + b = 0, where 'a' and 'b' are constants, and 'x' is the variable.
Example: 2x + 3 = 7
Quadratic Equations:
A quadratic equation is an equation in which the highest power of the variable is 2.
The general form of a quadratic equation in one variable 'x' is: ax^2 + bx + c = 0, where 'a', 'b', and 'c' are constants, and 'x' is the variable.
Example: x^2 - 5x + 6 = 0
Simultaneous Equations (Linear):
Simultaneous equations involve two or more equations with multiple variables, and the goal is to find the values of all the variables that satisfy all the given equations simultaneously.
Example:
2x + y = 8
3x - 2y = 7
Exponential Equations:
Exponential equations involve variables in the exponent, and the goal is to find the value of the variable.
Example: 2^x = 16
Trigonometric Equations:
Trigonometric equations involve trigonometric functions like sine, cosine, tangent, etc., and the goal is to find the values of the variable that satisfy the equation.
Example: sin(x) = 0.5
Solving equations in the Quantitative Ability section often requires algebraic manipulation, factoring, substitution, and application of various mathematical concepts. Practice and familiarity with different types of equations are crucial to excel in this section of quantitative aptitude tests and examinations.
