What is the value of m when the equation x2 + MX-3 = 0 has a common root with the equation x2-4x - (m-1) = 0? And find the common root

What is the value of m when the equation x2 + MX-3 = 0 has a common root with the equation x2-4x - (m-1) = 0? And find the common root

Let the common root be α. Then the two roots of the equation x2 + MX-3 = 0 are α, - M - α; the two roots of the equation x2-4x - (m-1) = 0 are α, 4 - α. The relationship between the root and the coefficient is: α (- M - α) = - 3 ①, α (4 - α) = - (m-1) ②. From ②, M = 1-4 α + α 2 ③, and substituting ③ into ①, α 3-3 α 2 + α -

When m is a value, the equation x ^ 2 + MX-3 = 0 and the equation x ^ 2-4x - (m-1) = 0 have a common root
There are two ways, please help me solve this problem: x ^ 2 + MX-3 = x ^ 2-4x - (m-1), if not, please help me solve another problem

By solving the equation x ^ 2 + MX-3 = x ^ 2-4x - (m-1), x = 4-m / 4 + m is substituted into the original equation
When m ^ 3 + 2m + 16m + 32 = 0, decompose (m ^ 2 + 16) (M + 2) = 0 of the factor to get m = - 2, x = 3 is the common root

What is the value of m when the equation x2 + MX-3 = 0 has a common root with the equation x2-4x - (m-1) = 0? And find the common root

Let this common root be α. Then the two roots of the equation x2 + MX-3 = 0 are α, - M - α; the two roots of the equation x2-4x - (m-1) = 0 are α, 4 - α. The relationship between the root and the coefficient is: α (- M - α) = - 3 ①, α (4 - α) = - (m-1) ② M = 1-4 α + α 2 ③, substituting ③ into ① to get: α 3-3 α 2 + α - 3 = 0, i.e. (α - 3) (α 2 + 1) = 0, α = 3. Substituting α = 3 into ③ to get: M = - 2. When m = - 2, the two equations have a common root, which is 3