Quantitative Aptitude ALGEBRA for IBPS PO & CLERK

Quantitative Aptitude ALGEBRA for IBPS PO & CLERK

Basic Formulas:

• (a + b)² = a² + b² + 2ab
• (a – b)² = a² + b² – 2ab
• (a + b)³ = a³ + b³ + 3ab (a + b)
• (a – b)³ = a³ – b³ – 3ab (a – b)
• a² – b² = (a – b) (a + b)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• a³ + b³ = (a + b) (a² – ab + b²)
• a³ – b³ = (a – b) (a² + ab + b²)
• a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ca)

if a + b + c = 0

• a³ + b³ + c³ = 3abc

Remainder theorem: If f(x) is divided by(x – a), then the remainder is f(a).

Factor theorem: If (x – a) is the factor of f(x), then f(a) = 0.

Linear Equations:

A Linear equation is one in which each variable occurs only in its first power & not in any higher powers. Generally, we have

• One equation in one unknown
• Two equations in two unknowns
• Three equations in three unknown

The general form of a system of linear equations in two variables x and y is

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Set of Equations:

1. Consistent set of equations: Those set of equations which have solutions.

Further, these set of equations can have a unique solution if

Condition: a¹ / a² ≠ b¹ / b²

These set of equations can have infinite number of solutions if

Condition: a¹ / a²= b¹ / b²= c¹ / c²

2. Inconsistent set of equations: Those set of equations which have no solution.

Condition: a¹ / a² = b¹ / b² ≠ c¹ / c²

Quadratic Equations:

A Quadratic equation is one in which each variable occurs only in its second power.

General form of quadratic equation is

ax² + bx + c = 0

Roots are– b +  / 2a, – b –  / 2a

Sum of roots = -b / a

Product of roots = c /a

Nature of roots

• If b² – 4ac = 0 roots are real and equal
• b² – 4ac > 0 roots are real and distinct
• b² – 4ac < 0 roots are imaginary

Forming Equation from roots:

If α and β are the roots of any quadratic equation then that equation can be written in the form

x² – (α + β)x + αβ = 0

i.e. x² – (sum of the roots) x + Product of the roots = 0.

Maximum /Minimum value of Quadratic Equation:

The equation ax² + bx + c = 0, will have maximum value when a < 0 and minimum value when a > 0.

The maximum or minimum values are given by

4ac − b² / 4a

, and will occur at x =-b / 2a

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