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The roots of the equation
[tex]8x ^{2} - x + 2 = 0[/tex]
are
[tex] \alpha [/tex]
And
[tex] \beta [/tex]
While the roots of the equation

The roots of the equation tex8x 2 x 2 0texare tex alpha texAnd tex beta texWhile the roots of the equation class=

Respuesta :

for the first equation αβ = 2/8 = 1/4   and α+β = -(-1/8) = 1/8

for the second equation  (α-2)(β -2)  = n/m and  (α-2 + β-2) =  3/m

(α-2)(β -2) = 
αβ + 4 - 2(α+β)  Substituting values for αβ and α+β obtained earlier we have:-
1/4 + 4 - 2(1/8) = 4 1/4 - 1/4  = 4  
so n/m = 4......................................(1)

(α-2 + β-2) = α + β - 4 = 1/8 - 4 = -3 7/8 = 3 / m
so 3 / m  = -3 7/8 .............................(2)

from equation (2):-    m =  -24/31

and therefor n =  4 * -24/31 = -96/31


The algebra is a bit messy  but i think its right

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