# How do you find the discriminant and how many and what type of solutions does #4x^2+ 9 = 0# have?

##### 1 Answer

#### Explanation:

Given:

#4x^2+9 = 0#

Note that we can also write this as:

#4x^2+0x+9 = 0#

which is in the standard form:

#ax^2+bx+c = 0#

with

This has discriminant

#Delta = b^2-4ac = (color(blue)(0))^2-4(color(blue)(4))(color(blue)(9)) = 0-144 = -144#

Since

We can use the difference of squares identity:

#A^2-B^2 = (A-B)(A+B)#

with

where

#0 = 4x^2+9#

#color(white)(0) = (2x)^2+3^2#

#color(white)(0) = (2x)^2-(3i)^2#

#color(white)(0) = (2x-3i)(2x+3i)#

Hence:

#x = +-3/2i#