Quadratic equations with complex roots

                  Quadratic equations with complex roots are quadratic equations with discriminant is less than zero. While solving a quadratic equation we will get either real or imaginary roots. The following sub-topic Nature of roots describes the conditions when we will get real roots, equal roots, and complex roots.

Nature of roots: 

  1. When the discriminant is equal to zero then the roots are equal and real.
  2. When the discriminant is less than zero, then we will get negative number under the square root. So we will get complex roots.
  3. When the discriminant is greater than zero, then we will get real and distinct roots.

The discriminant of a quadratic equation ax2+bx+c=0 is b2-4ac.

       When this discriminant is negative which is under square root we will get a complex number.


Solve: x2+4x+5=0

           Here  a = 1, b=4 and c=5 

So before start solving the equations, let us find the value of the discriminant which tells us about the nature of the roots. We will see another example in which we will solve a quadratic equations with complex roots.

Example 2:

        Find the solution of the given equation.

Using the above method student can practice  problems given below to master in solving quadratic equations.

Practice problems:

  1. Solve for x and express the roots of the equation in the complex form a+ib
            x2⁄2 = 2x+4

       2. Find the solution set of the given equation, say whether they are real or complex.


More problems are discussed in worked out problems page. Teachers and parents can guide the student to practice the problems and get a good knowledge about the complex numbers. If you have any doubt in any problem, you can contact us, we will clear all your doubts.

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