Using Complex Numbers in Solving Quadratics

There are two particular types of quadratic equations where the use of complex numbers becomes necessary. The first type includes quadratic equations in which there is no linear term and the squared term is set equal to a negative number. The second type occurs when the discriminant in the quadratic equation is negative.

Type 1: Solve .

• Take the square root of both sides of the equation.



• Simplify.

When dealing with a negative number under the square root, we have to make use of imaginary numbers. To learn more about imaginary numbers click here.

Type 2: Solve

• Use the quadratic formula: where a = 1, b = -3, and c = 10







and