Question

Please help! Find the zeros of the function
f(x) = x^3 + 2x^2 + x - 2

Answer 1

well I just graphed it... and it has 1 zero...

Answer 2

and given f(0) = -2

and f(1) = 2

the zero is between x = 0 and x = 1

so perhaps the half interval method or Newton's method could be used to approximate the zero...

Answer 3

I've never heard of either of those methods.

Hey can I do this:

if I find the zeros for g(x) = x^3 + 2x^2 + x

0 = x(x^2 + 2x + 1)
x = 0, x = -1

But then subtract those by -2 since g(x) is a vertical translation of f(x)

So the zeros of f(x) are x = -2 and x = -3?

But isn't there a way to solve this using algebra?

Answer 4

Actually I graphed it and it says the zero is at 0.7
but I have no idea how to get that answer

Answer 5

ok.... well a really easy solution is to graph the curve... that will give you the zero...


well the translation is down 2 so the zero of x =-1, as its a perfect square so only touches at x = -1, will now disappear... and the zero at x = 0 moves right....

Answer 6

So there isn't a way to solve this using basic algebra or algebra 2?

Answer 7

Like the way you'd solve another function that can be factored or something

Answer 8

well the problem is the curve doesn't have a rational root...

Answer 9

using the rational root theorem

the possible rational roots are

-1, 1, -2, and 2

none of those give f(x) = 0

so the root, is irrational...

Answer 10

That makes sense

Answer 11

there is probably a solution, but I haven't come across it

Answer 12

So I should estimate it as 0.7 because I can't solve it algebraically right?

Answer 13

We haven't learned that integral calculus stuff you said

Answer 14

well I graphed it using

https://www.desmos.com/calculator

and it gave me x = 0.696

Answer 15

newton's method is differential calculus... its used to approximate the roots by using iterations.

Answer 16

fun stuff I"ll have to learn later. Well thanks for helping me with this problem :]

Answer 17

good luck