Calculate the range of values of $\displaystyle c$ for which $\displaystyle 3x^2 - 9x + c > 2.25$ for all values of $\displaystyle x$.
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Hint: $\displaystyle 3x^2 - 9x + (c - 2.25)\ne0$ for all values of $\displaystyle x$ iff the discriminant of the quadratic polynomial is negative.