Find all numbers k such that x2 2x k 0 has no real soluti

Find all numbers k such that x² + 2x + k = 0 has no real solutions.

Solution

x² + 2x + k = 0

=>x² + 2x = -k

=>x² + 2x +1 = 1-k

=>(x+1)²=(1-k)

=>x+1=±(1-k)

=>x=-1±(1-k)

x² + 2x + k = 0 has no real solutions when 1-k <0

=>k>1

x² + 2x + k = 0 has no real solutions for k=(1,)