Given that the root of an the equation \(2x^2 + (k+2)x+k=0\) is 2, find the value of k

Given that the root of an the equation \(2x^2 + (k+2)x+k=0\) is 2, find the value of k

Answer Details

If 2 is a root of the equation \(2x^2 + (k+2)x+k=0\), then we can substitute x = 2 into the equation and get: \[2(2)^2 + (k+2)(2) + k = 0\] Simplifying this gives: \[8 + 2k + 4 + k = 0\] \[3k = -12\] \[k = -4\] Therefore, the value of k is -4.