Question

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

Answer 1

Answer:

k = -10

Step-by-step explanation:

α+β = -k/3                     (Sum of roots is -b/a) -----(1)

αβ = 8/3                        (Products of roots is c/a) ----(2)

α/β = 2/3                       (Given) -----(3)

Multiplying Equations (2) and (3),

α^2 = 16/9

=> α = 4/3 -----(4)

From (3) and (4),

β = 2 -----(5)

Finally, from (1), (3), and (4),

4/3 + 2 = -k/3

10/3 = -k/3

Therefore, k = -10

Hope it helps!