For the equation kx^2-(1+k)x+(3k+2)=0, the sum of the roots is twice their product. find k and the 2 roots

The value of k is

The roots are -1 and

Step-by-step 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

∴

∴ ⇒Multiply both sides by k

1 + k = 6k + 4⇒ 1 - 4 = 6k - k

5k = -3 ⇒

Use the value of k in the equation:

⇒ 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

the answer to this question is 3/19

step-by-step explanation: