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Free APTITUDE Practice | ALGEBRA | QUANTITATIVE APTITUDE

Free APTITUDE Practice | ALGEBRA | QUANTITATIVE APTITUDE

Online Bank Exam Preparation – Quantitative Aptitude – ALGEBRA

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

  1. 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 areb +  / 2a, b –  / 2a

Sum of roots = -b / a

Product of roots = c /a

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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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February 5, 2018

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