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mathmath333
 one year ago
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mathmath333
 one year ago
The question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1Find how many integers \(a\) are there such that \(\large \color{black}{\begin{align} 9x^2+3ax+a+5>0,\ x\in \mathbb{R} \hspace{.33em}\\~\\ \end{align}}\) for all values of \(x\). \(\large \color{black}{\begin{align} &a.) \ 7\hspace{.33em}\\~\\ &b.) \ 8\hspace{.33em}\\~\\ &c.) \ 9\hspace{.33em}\\~\\ &d.) \ 10\hspace{.33em}\\~\\ \end{align}}\)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3i think you need to solve \[a^24a20<0\] for that parabola to be >0 since the leading coefficient is >0 must be above xaxis so for that to be true the discriminant must be less than zero

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3so we need to draw the parabola a^24a20 to see the range of integers where it is <0

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3according to this picture here https://www.desmos.com/calculator the range for a such that a^24a20<0 2.9<a<6.9 how many integers are there in that range

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3looks like 9 to me

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3took me to time to realize this!

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3but i might be wrong for my skills lol
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