Without solving examine the nature of the roots of the equation:
$2 x^{2} - 5 x + 5 = 0$

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Solution

Step 1: Nature of the roots of an equation.
The given equation is as follows:
$2 x^{2} - 5 x + 5 = 0$
Compare the co-efficient of the given equation with $a x^{2} + b x + c = 0$ to get:
$a = 2, b = - 5 and c = 5$
Now solving for discriminant as:
$\begin{array}{rcl} ∴ D & = & {(b)}^{2} - 4 a c \\ = & {(- 5)}^{2} - 4 (2) (5) \\ = & - 15 \\ D & = & - 15 < 0 \end{array}$
Hence, the roots of the given equation are imaginary.

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