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The graph of the equation $y=ax^2+bx-6$ is completely below the $x$-axis. If $a^2=4$, what is the largest possible integral value of $b$?

 Aug 7, 2023
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y =ax^2 + bx  - 6

 

a^2 = 4

 

If this lies  completely below the   x axis, then a must  be negative because the  parabola will  turn  downward

 

So....a^2 =4  and  a  = -2

 

Since this lies  below the  x axis it  will  have no  real  roots....therefore, the discriminant  must  be < 0

 

b^2 - 4(-2)(-6)  < 0 

 

b^2  -48 < 0

 

b^2 < 48

 

b < 7  →     the largest value of b  =  6

 

 

cool cool cool

 Aug 8, 2023

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