Question #8d622

1 Answer
May 8, 2017

Answer:

#0#

Explanation:

We have:

# f(x) = 3x^2+3x+2 #

An #x#-intercept occurs when #f(x)=0#

# => 3x^2+3x+2 = 0 #

To solve this quadratic we could compete the square or use the quadratic formula,

We can also use the discriminant #Delta=b^2-4ac# to determine the nature of the roots of #ax^2+bx+c=0#, as:

If # Delta=b^2-4ac \ { (lt 0, "no real roots"), (=0, "two equal real roots"), (gt 0, "two distinct real roots") :}#

For our equation we have:

# Delta = 3*3-4*2*2 < 0 #

Hence there are no real solutions, and therefore #0# #x#-intercepts.

We can confirm this graphically:
graph{3x^2+3x+2 [-5, 5, -2, 5]}