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The graph of the equation y=ax^2+bx-18 is completely below the x axis. If , a^2=49 what is the largest possible integral value of b?

 Dec 1, 2020
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If this graph is  completely below  the x axis, then a   must  =  -7

 

So we have

 

-7x^2  + bx   - 18

 

And since  it lies below the x axis  the roots are complex.....so we  want to find the largest  value of b  such that the discriminant is <  0.....so.....

 

b^2  - 4(-7)(-18)  <  0

 

b^2  - 504 <   0

 

b^2  <  504

 

b <  floor [sqrt (504)]    =  22

 

So  b  = 22   is the largest  integer balue  for b that will guarantee that the function lies nelow the  x axis

 

See the graph here  : https://www.desmos.com/calculator/lhbvrcjkmg

 

 

cool cool cool

 Dec 1, 2020

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