4 Maths Forumulae

8/12/2019 4 Maths Forumulae

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1. (a + b)2

= a2

+ 2ab + b2

2. (a - b)2 = a22ab +b2

3. (a2- b2) = (a + b) (a b)

4. (a + b + c)2 = a2+ b2+ c2+ 2ab + 2bc +2ca

5. (a + b)3= a3+ b3+ 3ab (a + b)

6. (a b)3= a3b33ab (a b)


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7. a3

+ b3

= (a + b) (a2

- ab + b2

)8. a3b3= (a b) ( a2+ ab + b2)

9. a3

+ b

3

+ c

3

3abc = (a + b + c) (a

2

+ b

2

+ c

2

ab

bc

ca)

10. a4- b4= (a + b) (a b) (a2+ b2)

11. a4

+ b4

= (a2

-2 ab + b2

) (a2

+2 ab + b2

)

12. (a4+ a2b2+ b4) = (a2ab + b2) (a2+ab +b2)


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1. General form: ax2+bx +c =0

where a, b, c are real a=0

2. There are two roots or solutions for a

quadratic equation.3. The roots / solutions can be found by

Factorization Method or Formula Method.

4. Formula Method:

The solutions arex= (- b b24ac) / 2a


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Discriminant Nature of the roots

> 0 and a perfect square Real, distinct & rational

> 0 and not a perfect square Real, distinct & irrational

= 0 Real, rational & equal

< 0 Unreal (complex or imaginary)

5. Nature of the roots: The nature of the roots

depends upon the value of b24ac. Therefore b

24ac

denoted by is called the discriminant of the quadratic

equation


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6. Relation between roots and coefficients:

If and are the roots of the equation ax2+ bx+ c =0

thena) Sum of roots + = b/a

= - (coefficient ofx) / ( coefficient ofx2 )

b) Product of roots = c/a= constant term / coefficient of x2

c) Formula for forming an equation with known roots:

If and are the roots then the corresponding quadraticequation is,

x2x(sum of the roots) + (product of the roots) = 0

i.e. x2

x(+ ) + () = 0


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Arithmetic Progressions:

n = No. of terms

a = first term

d = Common difference(c.d)

1. nthterm =a+(n-1) d

2. Sum of nterms = n/2 [2a + (n - 1) d] = n/2 (a + l)

or n / 2 [1st term +last term]


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Special Sequences:

3. Sum of nnatural numbers

n = 1+2+3++n = [ n (n + 1) ] / 2

4. Sum of squares of first n natural numbers

n2=12+22+32+..+n2= [ n (n + 1)(2n + 1)] / 6

5. Sum of cubes of first n natural numbers

n3= 13+23+33++n3= [n (n + 1) / 2] 2


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Geometric progressions:

6. nthterm of G.P = a rn -1

where r = common ratio

7. Sum of nterms of G.P

Sum = a (rn-1) / (r 1) for r > 1

Sum = a (1- rn) / (1 r) for r < 1

Sum to infinity = a / (1 r) for r < 1


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Harmonic Progression:

8. a1, a2, a3are in H.P.

if 1/a1, 1/a2, 1/a3are in A.P.


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For further informationcontact:


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INFOSYS, WIPRO, SATYAM, CTS, TCS, HCL

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