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**Hint:**The nature of the roots depends on the value of the discriminant of the quadratic equation.

$a{x^2} + bx + c = 0$, where $a \ne 0$

Find the Discriminant, $D = {b^2} - 4ac$ , of the given quadratic equation, and check the sign (i.e. positive or negative or zero) to know if there are two solutions or one solution or no solution.

**Complete step-by-step answer:**

Step 1: Given the quadratic equation:

$2{x^2} - 3x + 5 = 0$

On comparing with standard quadratic equation: $a{x^2} + bx + c = 0$, where $a \ne 0$

a = 2, b = -3, c = 5

Step 2: Find discriminant:

$D = {b^2} - 4ac$

$D = {\left( { - 3} \right)^2} - 4 \times 2 \times 5$

$

\Rightarrow {\text{ }} = 9 - 40 \\

\Rightarrow {\text{ }} = - 31 \\

$

Step 3: Check the sign of discriminant:

$D < 0$

Hence, the roots are imaginary.

Final answer: The roots of $2{x^2} - 3x + 5 = 0$ are not real. Thus the correct option is (C).

**Additional Information:**

Roots of the quadratic equation is given by:

Quadratic equation: $a{x^2} + bx + c = 0$, where $a \ne 0$

Roots: \[x = \dfrac{{ - b \pm \sqrt D }}{{2a}}\]

The imaginary roots of the given quadratic equation are:

$2{x^2} - 3x + 5 = 0$

D = -31

\[x = \dfrac{{ - b \pm \sqrt D }}{{2a}}\]

$

{\text{ }}x = \dfrac{{ - \left( { - 3} \right) \pm \sqrt {\left( { - 31} \right)} }}{{2\left( 2 \right)}} \\

\Rightarrow {\text{ }} = \dfrac{{3 \pm {\text{i}}\sqrt {31} }}{4} \\

$

**Note:**For quadratic equation: $a{x^2} + bx + c = 0$, where $a \ne 0$

Let $y = f\left( x \right) = a{x^2} + bx + c = 0$

Discriminant, $D = {b^2} - 4ac$

A discriminant of zero indicates that the quadratic has a repeated real number solution.

i.e. $D = 0$ , roots are real and equal.

$ \Rightarrow {b^2} - 4ac = 0$

A positive discriminant indicates that the quadratic has two distinct real number solutions.

i.e. $D > 0$ , roots are real and unequal.

$ \Rightarrow {b^2} - 4ac > 0$

A negative discriminant indicates that neither of the solutions is real numbers.

And if D < 0, as in the case of the given question, roots are imaginary.

$ \Rightarrow {b^2} - 4ac < 0$

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