Solve the quadratic equation 2 x 2 + x + 2 = 0 .

The given equation is 2 x 2 + x + 2 = 0 Let the roots are α & β Comparing it with the standard equation a x 2 + b x + c = 0 a = 2 , b = 1 , c = 2 Using the quadratic formula the roots are given by α , β = - 1 ± - 1 2 - 4 × 2 × 2 2 2 α , β = - 1 ± 1 - 8 2 2 α , β = - 1 ± - 7 2 2 Therefore, - 1 + i 7 2 2 , - 1 - i 7 2 2 are the required roots.

Solve the quadratic equation 5 x 2 + x + 5 = 0 .

The given equation is 5 x 2 + x + 5 = 0 Let the roots are α & β Comparing it with the standard equation a x 2 + b x + c = 0 a = 5 , b = 1 , c = 5 Using the quadratic formula the roots are given by α , β = - 1 ± 1 2 - 4 × 5 × 5 2 5 α , β = - 1 ± 1 - 20 2 5 α , β = - 1 ± - 19 2 5 Therefore, - 1 + i 19 2 5 , - 1 - i 19 2 5 are the required roots.

Solve the quadratic equation x 2 - 2 x + 3 2 = 0 .

The given equation is x 2 - 2 x + 3 2 = 0 Let the roots are α & β Comparing it with the standard equation a x 2 + b x + c = 0 a = 1 , b = - 2 , c = 3 2 Using the quadratic formula the roots are given by α , β = - - 2 ± - 2 2 - 4 × 1 × 3 2 2 × 1 α , β = 2 ± 4 - 6 2 α , β = 2 ± i 2 2 Therefore, 1 ± i 1 2 are the required roots.