SOLUTION: Given the function {{{f(x)=2x^2+mx+27}}} and f(x)<0 when {{{3<x<n}}}. Find the values of m and n

Question 1135305: Given the function and f(x)<0 when . Find the values of m and n
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the function is negative when (3 < x < n), then 3 and n must be zeroes of the function.

if we assume that 3 is one of the zeroes, then f(3) must be equal to 0.

when x = 3, the equation becomes 2 * 3^2 + m * 3 + 27 = 0

this then becomes 18 + 3m + 27 = 0 which becomes 3m + 45 = 0 which results in m = -15.

the equation becomes 2x^2 - 15x + 27 = 0.

factor this equation to get (2x - 9) * (x - 3) = 0

solve for x to get x = 3 or x = 4.5.

you get m = -15 and n = 4.5.

here's the graph.

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