Answer:
The value of k is

The roots are -1 and

Explanation:
In any quadratic equation
the sum of its roots is
and the product of its root is

In the equation

The sum is

The product is

∵ The sum of the roots is twice their product
∴
![(k+1)/(k)=2[(3k+2)/(k)]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ihdybvltt28px0m85fmkwzmw5py5mmptzz.png)
∴
⇒Multiply both sides by k
1 + k = 6k + 4⇒ 1 - 4 = 6k - k
5k = -3 ⇒

Use the value of k in the equation:
![(-3)/(5)x^(2)-[1+(-3)/(5)]x+[(3)((-3)/(5))+2]=0](https://img.qammunity.org/2020/formulas/mathematics/middle-school/706gn2fjk2elx8m43m94bw6wq5rbdfb0e5.png)
⇒ Multiply equation by 5
⇒ Multiply equation by -1
⇒ use factorization to find roots
(3x - 1)(x + 1) = 0
3x -1 = 0⇒ 3x = 1⇒ x = 1/3
x + 1 = 0⇒ x = -1
The roots are 1/3 and -1