What is the nature of the roots of this equation:

${ 2x }^{ 2 }-4x+7=2$

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Check out the set:
2016 Problems
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Real and Distinct
Not Real
Real and Equal

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$\begin{array}{c}2x^2 - 4x + 7 = 2 \\ 2x^2 - 4x + 5 = 0 \\ {\text{The discriminant will determine, which kind of roots does given equation has.}} \\ D = b^2 - 4ac = 16 - 40 = -24 < 0 \\ {\text{Since, the discriminant is negative, so the roots will be imaginary, hence}} \color{#EC7300}{\boxed{{\text{not real}}}} \end{array}$