The roots of the equation 8x ^(2) - x + 2 = 0 are \alpha And \beta While the roots of the equation

Question

The roots of the equation


`8x ^(2) - x + 2 = 0`
are

`\alpha`
And

`\beta`
While the roots of the equation

Answer 1

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