Question

if alpha and beta are the roots of the equation 3x2+kx+8=0 and alpha/beta = 2/3 find value of k . k>0

Answer 1

Heya User,

--> α/β = 2/3 --> ( i )


[ We use the "Co-efficient - Zeroes relation / also known as Viete's Relation ] --> 

--> α * β = 8/3 --> ( ii )

--> Multiplying ( i ) with ( ii ) --> 
 ---> α² = 16 / 9
  => α = ± ( 4/3 )

Correspondingly, β = ± 2

Further, we have the relation, α + β = -k / 3
         => ± [ 4/3 + 2 ] = -k / 3
         => ± [ 10 / 3 ] = - k / 3
         => k = - 10 or +10 

However, since, k > 0, k = 10 for α = -4/3 || β = -2 is considered the reqd. value.