find the number of possible positive real zeros of f(x)=8x^4-72x^3+144x^2

Question

paxpolaris · Answer

$$\large f(x)=8x^4-72x^3+144x^2 $$
 is this it?

anonymous · Answer

yes

paxpolaris · Answer

$$\large f(x)=8x^2\left( x^2-9x+18 \right)$$

anonymous · Answer

wait so what do i do?? im so confuseddd

paxpolaris · Answer

we can see that f(x)=0 has 1 repeated  at x=0.  

next we can check if there are any positive solutions to x^2-9x+18=0

paxpolaris · Answer

$$\large f(x)=8x^2\left(x-6 \right)\left( x-3 \right)$$

^^^ that's the factored form of f(x) ... correct ?

paxpolaris · Answer

so $f(x)=0$ when $x=0, 6 ,$ or $3$

paxpolaris · Answer

so there are $\Large 2$ positive, real zeroes : 3 and 6.

anonymous · Answer

ohhhh okay, so whenever there is a 0 with problems like this it doesnt count as a positive real zero right ?

paxpolaris · Answer

0 is real ... but not positive.

anonymous · Answer

oh okay!! thank you so much !

paxpolaris · Answer

but .... the question  isn't asking you actually find the zeroes ... just how many are positive and real.

there is a way to do that... even when f(x) can't be so easily factored:
www.purplemath.com/modules/drofsign.htm