This is a free lesson from our course in Algebra II
This lesson explains how to solve quadratic equation that has imaginary roots. When you look at the write up; may
find difficult to comprehend but once go through some examples with solution, and
the instructor's explanation with the help of audio, video presentation in own hand
writing, you will find it easier. A root of an equation is a solution of that equation.
When the roots of a quadratic equation are imaginary, they always occur in conjugate
pairs i.e. the two solutions of equation are complexconjugates of each other.You have learnt earlier that
the discriminant of the quadratic formula is
b^{2}  4ac.
If the discriminant is negative, when you solve the quadratic equation it forms
complex roots.
(More text below video...)
(Continued from above)
You can find out the roots using the quadratic
formula applying
x = {b
(b^{2}
– 4ac )}/ 2a.
Since discriminant is a negative number, if the given equation is to be solved there
would be two conjugate complex (imaginary) solutions.
To write the answer in a + bi form remove the common factors and
then write b as a coefficient of i. For example, find the roots of
the quadratic equation 3x^{2} + 4x + 8 = 0. x = {4
(4^{2}
– 4(3)(8) )}/ 2(3). x = {4
(16
–96 )}/ 6 x = {4
(–80)}/
6 x = {4
4i5}/6 x = {2
2i5}/
3 x = 2/3
+
(2i5)/3,
2/3 
(2i5)/3.
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