Algebra-1.txt

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Author:
sjs.vikrant
ID:
283326
Filename:
Algebra-1.txt
Updated:
2014-09-17 02:15:51
Tags:
algebra
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Description:
algebra
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  1. if in equation 
    A=C, then?
    two roots α and β are reciprocal to each other
  2. if in equation 
    B=0, then?
    two roots α and β are equal in magnitude and oposite in sign
  3. in equation x2+5x+6=0
    the sign of two roots α and β is ???
    • sign of (α and β)=  -ve
    • sign of (αβ)= +ve
    • both roots α and β are negative
  4. in equation x2-5x+6=0
    the sign of two roots α and β is ???
    • sign of (α and β)=  +ve
    • sign of (αβ)= +ve
    • so,both roots α and β are positive
  5. in equation x2-5x-6=0
    the sign of two roots α and β is ???
    • sign of (α and β)=  +ve
    • sign of (αβ)= -ve
    • then, α is positive and β is negative if  α>β(numerically)
  6. in equation x2+5x-6=0
    the sign of two roots α and β is ???
    • sign of (α and β)=  -ve
    • sign of (αβ)= +ve
    • then, α is negative and β is positive
    • if,  α>β(numerically)
  7. roots of an equation is given by
    x=(-b±√D)÷2a
  8. Nature Of Roots:
    If, D<0
    complex with non zero imaginary part
  9. Nature Of Roots:If,
    D=0
    rational and equal
  10. Nature Of Roots:If,
    D>0 and is a perfect square
    rational and unequal
  11. Nature Of Roots:If,
    D>0 and is NOT a perfect square
    irrational and conjugate pairs
  12. if in equation 
    A=1,   and B,C are integers
    and
    roots are rational numbers
    these roots must be integers
  13. if in equation
       and
     
    one root is common, then
  14. condition that , is factorizable into two linear factors
    when D0
  15. formation of a quadratic equation??
  16. nature of roots ??
    If D<0 then ???
    and D0 then , 
    • D<0   Imaginary
    • D0   Real

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