Complex Roots, solving a equation a+bi form

Question

What are the roots of the equation 9x²+24x+19+0, in simplest a+bi form.

Answer 1

If you set this up using quadratic formula where "a" = 9, "b" = 24, and "c" = 19, you will have the following:

x = [ -24 ± √ 24² - 4(9)(19) ]/ 18. Simplifying within the radical and rewriting the negative radicand in terms of i, you will have x = [ -24 ± 6i √3 ]/18, and this, once you separate the real and the imaginary parts and reduce the fractions, will simplify to x = -4/3 ± i √3/3.