Question

6.Using complete sentences, explain how to find the zeros of the function f(x) = 2x3 – 9x + 3. (2 points)

Answer 1

no i have to find the zeros

Answer 2

so first, what I find easiest is to factorise the equation:
f(x)=2x^3-9x+3

Answer 3

i just need one example of how to do it and then ican do the rest

Answer 4

when you can factorise the equation to this form:
y=(x-a)(x-b)(x-c), then your answers for zeros would be x=a, x=b, x=c
because it is a cubic

Answer 5

can you show me with an example?

Answer 6

I found this in my maths textbook, it teaches you how to factorise a cubic equation

Answer 7

let me explain. this part goes through remainder theorems and factor theorems, but I'm not sure if you've learnt that...

Answer 8

what you really need out of that is the long division. It'll help you to factorise your one.

Answer 9

the 1st step is to look at the back number, the one that doesn't have an x.
x^3-19x+30
in this case it is the 30.

the next step is to find factors of this number (start with the smaller ones)
1,2,3,5,6,10,15,30. Don't forget their negative counterparts: so -1,-2,-3 etc.

Answer 10

in the example they chose -5. which if you do x=-5, then your quadratic factor would be (x+5). it's the opposite

Answer 11

so it just goes through dividing it and then once in a quadratic, simplify it further to get 3 brackets.

Answer 12

so the zeros of the function would be x=-5, x=2, x=3 because
y=(x+5)(x-2)(x-3)
0=(x+5)(x-2)(x-3)
then (x+5)=0, (x-2)=0, and (x-3)=0.
so eventually the zeros of the function would be x=-5, x=2, x=3

Answer 13

OR!!! What you could do is make f(x)=0, then solve from there because I typed it into a calculator, but I got a decimal answer. So maybe factorising isn't the best thing to do. Sorry for ALL the confusion!!!