  #### Find whether the following equations have real roots. If real roots exist, find them.

(i) We Know that b2-4ac > 0 in the case of real roots and b2 - 4ac < 0  in the case of imaginary roots.

For the equation

Compare with where

a=8,b=2,c=-3

Hence the equation has real roots

Roots of the equation   are

(ii) We Know that b2-4ac > 0 in the case of real roots and b2 - 4ac < 0  in the case of imaginary roots.

For the equation

Compare with where

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

Hence the equation has real roots

Roots of the equation   are

(iii) We Know that b2-4ac > 0 in the case of real roots and b2 - 4ac < 0  in the case of imaginary roots.

For the equation

Compare with where

a=5,b=-2,c=-10

Hence the equation has real roots

Roots of the equation   are

(iv) We Know that b2-4ac > 0 in the case of real roots and b2 - 4ac < 0  in the case of imaginary roots.

For the equation

Compare with where

a=2,b=-16,c=23

Hence the equation has real roots

Roots of the equation are

(v) We Know that b2-4ac > 0 in the case of real roots and b2 - 4ac < 0  in the case of imaginary roots.

For the equation

Compare with where

Hence the equation has real roots

Roots of the equation   are