When k is a value, the two roots of the quadratic equation KX ^ 2 + 2kx + K-3 = 0 are negative roots

When k is a value, the two roots of the quadratic equation KX ^ 2 + 2kx + K-3 = 0 are negative roots

kx^2+2kx+k-3=0
If both roots are negative, the following three conditions must be satisfied
（1）△≥0
（2）x1+x2＜0
（3）x1×x2>0
So: (2k) & sup2; - 4K (K-3) ≥ 0
k≥0
From (2): X1 + x2 = - 2

If a and B are fixed values, the equation 2kx + a3 = 2 + X − bk6 about X, no matter what the value of K is, its root is always 1. Find the value of a and B

Both sides of the equation are multiplied by 6 at the same time to get: 4kx + 2A = 12 + x-bk, (4k-1) x + 2A + bk-12 = 0 ①, ∵ no matter what the value of K is, its root is always 1, ∵ substitute x = 1 into ①, 4k-1 + 2A + bk-12 = 0, then when k = 0, k = 1, we can get the equations: − 1 + 2A − 12 = 04 − 1 + 2A + B − 12 = 0, the solution is a = 132, B = - 4

Given that a and B are fixed values, the equation (2kx + a) / 3 = 2 + (x-bk) / 6 for X. no matter what the value of K is, it always has a root of 1, so we can find a + B

Then substitute x = 1 into (2k + a) / 3 = 2 + (1-bk) / 6
2(2k+a)=12+1-bk
4k+2a=13-bk
So 4 = - B, 2A = 13
So B = - 4, a = 13 / 2
So a + B = 13 / 2-4 = 5 / 2

If a and B are fixed values, the equation 2kx + a3 = 2 + X − bk6 about X, no matter what the value of K is, its root is always 1. Find the value of a and B

If both sides of the equation multiply by 6 at the same time, we can get: 4kx + 2A = 12 + x-bk, (4k-1) x + 2A + bk-12 = 0, ①, ∵ no matter what the value of K is, its root is always 1, ∵ substitute x = 1 into ①, 4k-1 + 2A + bk-12 = 0, then when k = 0, k = 1, we can get the equation system: − 1 + 2A − 12 = 04 − 1 + 2A + B − 12 = 0, the solution is a = 132, B = - 4, when a = 132, B = - 4, no matter what the value of K, its root is always 1

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You don't need any reason to love someone. You will sacrifice everything for her

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I never knew that I would love someone so seriously

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Like is a feeling,but love is a kind of responsibility.

English translation
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I hope I could spend the rest of my life with you.
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