If x1, X2 are two real roots of the equation X2 (2k + 1) x + K + 1 = 0, and x1, X2 are greater than 0 If x 1 / x 2 = 1 / 2, find the value of K How to use the condition X1 / x2 = 1 / 2?

If x1, X2 are two real roots of the equation X2 (2k + 1) x + K + 1 = 0, and x1, X2 are greater than 0 If x 1 / x 2 = 1 / 2, find the value of K How to use the condition X1 / x2 = 1 / 2?

Is it x ^ 2 + (2k + 1) x + K + 1 = 0?
From X1 / x2 = 1 / 2, we can get X1 = 2x2, and X1 + x2 = - (2k + 1), x1x2 = K + 1,
That is, 3x1 = - (2k + 1), X1 ^ 2 = K + 1,
Then substitute X1 = - (2k + 1) / 3, X1 ^ 2 = K + 1 (that is, x = - (2k + 1) / 3, x ^ 2 = K + 1) into x ^ 2 + (2k + 1) x + K + 1 = 0 to get (k + 1) ^ 2 - (2k + 1) ^ 2 / 3 + K + 1 = 0, and finally get k value