SOLUTION: Find the values of b such that the equation below always gives real solutions. -3x^2 + bx -1 = 0

Algebra ->  Equations -> SOLUTION: Find the values of b such that the equation below always gives real solutions. -3x^2 + bx -1 = 0      Log On


   



Question 1127899: Find the values of b such that the equation below always gives real solutions.
-3x^2 + bx -1 = 0

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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To satisfy the problem's requirement, the discriminant of the equation must be non-negative:


b%5E2+-+4ac >= 0,


b%5E2+-+4%2A%28-3%29%2A%28-1%29 >= 0,


b%5E2+-+12 >= 0,


b%5E2 >= 12  ====>   b >= sqrt%2812%29 = 2%2Asqrt%283%29   OR   b <= -sqrt%2812%29 = -2%2Asqrt%283%29.


Answer.  The necessary and sufficient condition for "b"  is  |b| >= 2%2Asqrt%283%29 =~ 3.464102 .

Solved.