If α and β are roots of the equation x 2 + 8 x − 5 = 0, find he quadratic equation whose roots are α β , β α .

Question

If α and β are roots of the equation       x    2    +  8  x  −  5  =  0, find he quadratic equation whose roots are                     α                    β             ,                     β                    α            .

Katrina Fisher · Accepted Answer

x    2    +  8  x  −  5  =  0roots are   α  ,  β so  α  +  β  =  −  8  ,  α  β  =  −  5To find out eqn whose roots are             α      β       and             β      α       you need to find out its sum and multiplication  s  u  m  =            α      β        +            β      α        =                              α          2                +                  β          2                            α        β              =  s  o  l  v  e    i  t  ?you can find out above value: and  m  u  l  t  i  p  l  i  c  a  t  i  o  n  =            α      β        ×            α      β        =  1quadratic eqn =       x    2  -(sum of roots)x+multiplication of roots=0      x    2    −      (                  α        β              +                  β        α              )    x  +      (                  α        β              ×                  β        α              )    =  0

If alpha and beta are roots of the equation x^2+8x−5=0, find he quadratic equation whose roots are alphabeta , betaalpha

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