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

Question

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

Jakob Chavez · Accepted Answer

x    2    +  2  x  +  k  =  0    =&amp;gt;      x    2    +  2  x  =  −  k    =&amp;gt;      x    2    +  2  x  +  1  =  1  −  k    =&amp;gt;  (  x  +  1      )    2    =  (  1  −  k  )    =&amp;gt;  x  +  1  =  ±      (    1    −    k    )      =&amp;gt;  x  =  −  1  ±      (    1    −    k    )          x    2    +  2  x  +  k  =  0     h  a  s     n  o     r  e  a  l     s  o  l  u  t  i  o  n  s     w  h  e  n     1  −  k  &amp;lt;  0    =&amp;gt;  k  &amp;gt;  1        x    2    +  2  x  +  k  =  0     h  a  s     n  o     r  e  a  l     s  o  l  u  t  i  o  n  s     f  o  r     k  =  (  1  ,  i  n  f  t  y  )

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

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