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

Nica2t

Nica2t

Answered question

2022-08-05

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

Answer & Explanation

Jakob Chavez

Jakob Chavez

Beginner2022-08-06Added 14 answers

x 2 + 2 x + k = 0 => x 2 + 2 x = k => x 2 + 2 x + 1 = 1 k => ( x + 1 ) 2 = ( 1 k ) => x + 1 = ± ( 1 k ) => 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 < 0 => k > 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 )

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