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What real value of produces the smallest value of the quadratic t^2 - 9t - 36 + 3t^2 - t + 10?

 Apr 26, 2022
 #1
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The real value of t = 16/3 produces the smallest value.

 Apr 27, 2022
 #2
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Simplify it to: \(4t^2-10t-26\)

 

The least possible value occurs at: \(\large {-b \over 2a} \)

 

The quadratic equation is in the form \(ax^2+bx+c\) only difference being that we have t instead of x. 

 

Plugging in the values, we have the lowest real value occurs at \(\color{brown}\boxed{5 \over 4}\)

 Apr 28, 2022

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