SOLUTION: {{{ y = 6x^2 + bx + 11 }}} What is the smallest positive integer for b that will force this parabola to have two x-intercepts? Please show working

Question 985667:
What is the smallest positive integer for b that will force this parabola to have two x-intercepts?
Please show working
Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!

That will be when the discriminant is positive:

b�-4ac = b�-4(6)(11) > 0
              b�-264 > 0
                  b� > 264
              
Taking positive square roots:

                   b > 16.24807681

Smallest positive integer is the next higher positive integer, b=17.

When b=16, no x-intercepts:



When b=16.24807681, 1 x-intercept:



When b=17, 2 x-intercepts:



Edwin

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