SOLUTION: Find an interval for b that equation has at least 1 real solution x^2 + bx +64 = 0

For it, the discriminant of the quadratic function must be greater than or equal to zero,

which leads to inequality  


    b^2 - 4*64 >= 0.


It gives


    b^2 >= 256,   


with the solutions  b >= 16  OR  b <= -16.    ANSWER

It will have at least 1 real solution if its discriminant is non-negative.



has discriminant

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Solution: 

Edwin