   (i)     Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form   Where a, b and c are real numbers with

The given equation is

Here a=1,b=-3,c=4

Hence the equation has no real roots.

(ii)   Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Here a=2,b=-1,c=-1

Here for the equation

Hence it is a quadratic equation with two distinct real roots

(iii)   Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Here

here

Hence the equation have two real and equal roots.

(iv)    Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Here a=3,b=-4,c=1

Here

Hence the equation has distinct and real roots.

(v) Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Here

Hence the equation has no real roots.

(vi) Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Compare with where

Here

Hence the equation has two distinct real roots.

(vii)    Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Here

Here

Hence the equation has distinct real roots.

(viii) Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

compare with where

Here

Hence the equation has no real roots.

(ix) Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Here

Hence the equation has two distinct real roots.

(x) Quadratic equation : A quadratic equation in x is an equation that can be written in the standard form            Where a, b and c are real numbers with

The given equation is

Compare with where

Here

Hence the equation has two distinct real roots.