A Quadratic Equation will have equal roots if it satisfies the condition given below:
b² – 4ac = 0
Given equation is
x² + kx + k = 0
a = 1, b = k, x = k
On substituting in the equation we get,
k² – 4 ( 1 ) ( k ) = 0
k² – 4k = 0
k ( k – 4 ) = 0
k = 0 , k = 4
But by the given data we get to know that k is greater than 1.
Hence the value of k is 4 if the equation has common roots.
Hence if the value of k = 4, then the equation ( x² + kx + k ) will have equal roots.