Question

1. Determine the zeros of f(x) = x3 – 3x2 – 16x + 48? Somebody explain it please?:/

Answer 1

OH! I already know that there are 2or0 positive, 1 negative and 2or0 complex. But I dont know what to do next?

Answer 2

f(x) = x3 – 3x2 – 16x + 48 =x^2(x-3)-16(x-3) =(x-3)(x^2-16) = (x-3)(x-4)(x+4)
for f(x) =0
f(x) =(x-3)(x-4)(x+4) =0
x =3 , 4 , -4

Answer 3

are you familiar with rational roots theorem?

Answer 4

that the answer for all

Answer 5

...@abayomi12 that made no sense to me. I would like an explanation and @lgbasallote no I am not..

Answer 6

hmm...im trying to think of a way to solve this without using rational roots theorem. are you sure it was never taught to you before?

Answer 7

I'm doing virtual school. The online lesson isn't very clear about it. So if you have any other way to find the zero's that would be great!

Answer 8

well let me tell you about the general concept first..

the steps to finding the zeros of CUBIC functions are these:

Step 1: Find ONE factor of the expression

Step 2: Divide the expression by that factor (the quotient will be a quadratic equation)

Step 3: Factor or use the Quadratic Formula on that quadratic equation to get hte remaining roots

the rational roots theorem is used to find one of the factors for step 1

Answer 9

now as for an alternative method to rational roots theorem...i would have to ask for a consult from one of my colleagues.. @waterineyes would you be kind enough to grace us with your wisdom?

Answer 10

abayomi has the right idea in this case, try to factor the poly

Answer 11

try and error different combonations that have common factors to pull out

(x3 – 3x2) – 16x + 48?
x^2(x-3) -16x+48

it would be great of the (x-3) part is a factor of whats left on the right

n(x - 3)

xn - 3n = -16x+48
+16x +16x
--------------------
(n+16)x - 3n = 48
+3n +3n
---------------------
(n+16)x = 48 + 3n = 0

48 + 3n = 0
3n = -48
n = -16

if (-16+16)x = 0 , then we are good to go with this factoring ... most times this is done in the head tho