Question

if alpha and beta are roots of the equation 3 X square + kx + 8 is equal to zero and Alpha upon beta is equal to 2 by 3 then find the value of k​

Answer 1

3x^2 + kx + 8 = 0_______α,β

α/β = 2/3 => α = (2/3)β

We know, α + β = (-k)/3_______(1)

and α × β = 8/3 => (2/3)β × β = 8/3

=> β^2 = 4 => β = 2 or -2

=> α = 4/3 or -4/3

So, α + β = 2 + 4/3 or -2 -4/3

=> α + β = 10/3 or -10/3

Comparing these values with equation (1), we get

k = ±10