The nature of the roots of the quadratic equation 2x2-6x+9/2=0 is

Below.

Step-by-step explanation:

The value of the discriminant (b^2 - 4ac) will give you the nature of the roots.

ax^2 + bx + c = 0      - is the general form of a quadratic.

2x^2 - 6x + 9/2 = 0   Comparing with the above:

Here b = -6, a = 2 and c = 9/2 so:

the discriminant = (-6)^2 - 4*2*9/2

= 36 - 8 * 9/2

= 36 - 72/2

= 36 - 36

= 0

This tells us that the roots are real, rational and have multiplicity 2 ( duplicate roots).