Algebra-1.txt

  1. if in equation Image Upload 2
    A=C, then?
    two roots α and β are reciprocal to each other
  2. if in equation Image Upload 4
    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 Image Upload 6
    A=1,   and B,C are integers
    and
    roots are rational numbers
    these roots must be integers
  13. if in equation
     Image Upload 8  and
     Image Upload 10
    one root is common, then
    Image Upload 12
  14. condition that Image Upload 14, is factorizable into two linear factors
    when DImage Upload 160
  15. formation of a quadratic equation??
    Image Upload 18
  16. nature of roots ??
    If D<0 then ???
    and DImage Upload 200 then , 
    • D<0   Imaginary
    • DImage Upload 220   Real
Author
sjs.vikrant
ID
283326
Card Set
Algebra-1.txt
Description
algebra
Updated