Question

If a and ß are the roots of the quadratic equation 3x²+Kx+8=0 and alpha beta =. ⅔ then find the value of K.​

Answer 1

Answer:

alpha*beta = -b/a...(1)

but, alpha*beta= 2/3...........(2)(given)

-b/a= 2/3......(3).(from (1) and (2))

the eq is 3x2 +kx +8=0

comparing with general formula ax2+bx+c=0

a=3, b=k, c=8

-k/3=2/3.....(from (3))

-3k = 6

k=6/-3

k=-6/3

k= -2

the value of k is -2

hope it helps you

Answer 2

Answer:

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.