If x is real, the smallest value of the expression $$3x^{2}

1. If x is real, the smallest value of the expression $$3x^{2} - 4x + 7$$ is :

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By: anil on 05 May 2019 02.39 am

$$3x^{2} - 4x + 7$$ is the given quadratic equation
The smallest value of a given quadratic equation $$ax^2 + bx + c = 0$$ occurs at $$ x = dfrac{-b}{2a}$$
Thus, the smallest value of the given expression will occur at $$ x = dfrac{-(-4)}{2*3} = dfrac{2}{3}$$
Thus, the smallest vale of the given expression is $$3*(dfrac{2}{3})^2 - 4*(dfrac{2}{3}) + 7 = dfrac{19}{3}$$
Hence, option D is the correct answer.

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