Question

In which interval will the graph of f(x) = x³ – 9xÆ – 4x + 36 be below the x-axis?

Answer 1

hmmm since you may not have seen my post
about the last one you posted lemme repost

\(\large {
x^2 - 2x + 4 = 8x - 21\implies x^2-2x+4-8x+21=0
\\ \quad \\
x^2-10x+25=0\qquad notice\implies
\begin{array}{cccllll}
x^2&-10x&+25&=0\\
&\uparrow &\uparrow \\
&-5-5&-5\cdot -5
\end{array}
}\)

can you see how they factor?

Answer 2

-5 and -5 are factors of +25 => -5 * -5 = +25, thus

if you ADD THEM up, you get the middle term, -10
if you multiply them, you get the last term, +25
thus the factors would be -5 and -5
or
\(\bf (x{\color{brown}{ -5}})(x{\color{brown}{ -5}})\implies (x{\color{brown}{ -5}})^2\)

Answer 3

Did you get 25 from adding 21 and 4 ?

Answer 4

yeap \(\bf x^2 - 2x {\color{brown}{ +4}} = 8x {\color{brown}{ -21}}\implies x^2-2x{\color{brown}{ +4}}-8x{\color{brown}{ +21}}=0
\implies
x^2-10x{\color{brown}{ +25}}=0\)

Answer 5

but that's one way to factor a quadratic
you break down the last term, or the constant, into small factors
then mix and match see which SUM of 2 of those would give you the middle coefficient

Answer 6

Oh okay i see what you did there : ) . Thank you. So now can you help me with " In which interval will the graph of f(x) = x³ – 9xÆ – 4x + 36 be below the x-axis?"
I understand i set the equation to 0 but then what since i have a x cubed, squared and just a plain x ?

Answer 7

as far as this posting... is a cubic equation
meaning you may have to break it down into 3 binomials
but for that... you would have to use the ratiional root test and also the remainder theorem

and the exercise is of no use if you haven't covered those

Answer 8

unlesss you graph it. .and pick it from there, and that's another way

Answer 9

How would i graph it ? Im sorry for asking so many questions

Answer 10

well.. .you could use a graphing calculator
but if you're expected to find the roots first, and check their multiplicty
then you'd need the rational root test and remainder theorem

Answer 11

and there are many graphing calculators online
keep in mind that a computer is nothing but a big calculator
and there are many you could also install in your computer to run and check

Answer 12

Okay thanks ill put it in the calculator . Can you help me with some other problems ?

Answer 13

sure.. .just post anew.. thus if I dunno, someone else may, and we can revise each other :)

Answer 14

Thank you : )