Question

Where does the graph of this function cross the x-axis?
f(x)=x^2+14x+24/3x^2-11

Answer 1

@jim_thompson5910

Answer 2

The function is this right?
\[\Large f(x) = \frac{x^2+14x+24}{3x^2-11}\]

Answer 3

yes

Answer 4

First replace f(x) with 0. Then multiply both sides by \(\Large 3x^2-11\)
\[\Large f(x) = \frac{x^2+14x+24}{3x^2-11}\]
\[\Large 0 = \frac{x^2+14x+24}{3x^2-11}\]
\[\Large 0*(3x^2-11) = \frac{x^2+14x+24}{3x^2-11}*(3x^2-11)\]
\[\Large 0 = x^2+14x+24\]
\[\Large x^2+14x+24=0\]
Do you see how to solve from here?

Answer 5

Got it! (x+2)(x+12) right?

Answer 6

very good

Answer 7

so if (x+2)(x+12) = 0 then either x+2 = 0 or x+12 = 0

solve each equation for x to get your 2 answers

Answer 8

x=-2 and x=-12?

Answer 9

both are correct

Answer 10

All right, thank you so much!!

Answer 11

you're welcome