# How do you find the zeros, real and imaginary, of #y= 23x^2+18x-24# using the quadratic formula?

##### 1 Answer

Mar 27, 2018

There are two real roots:

# -9/23-sqrt(633)/23 # and# -9/23+sqrt(633)/23 #

#### Explanation:

We have:

# y = 23x^2+18x-24 #

So the roots are given by the solution of the equation:

# 23x^2+18x-24 = 0#

Using the quadratic formula:

# x = (-b+-sqrt(b^2-4ac))/(2a) #

With

# x = (-18+-sqrt(18^2-4(23)(-24)))/(2(23)) #

# \ \ = (-18+-sqrt(324+2208))/(46) #

# \ \ = (-18)/(46)+-sqrt(2532)/(46) #

# \ \ = -9/23+-sqrt(633)/23 #

Hence, there are two real roots:

# -9/23-sqrt(633)/23 # and# -9/23+sqrt(633)/23 #