Question

Determine if -1 is zero of the function above
f(x)=-4x^3-5x^2-7x+2

@zzr0ck3r

Answer 1

Use synthetic division.

Answer 2

@zzr0ck3r

Answer 3

well i did my division @Luigi0210 and i didnt find -1 is zero

Answer 4

i got it as not a rational function what would that mean would you be able to explain why exactly tho

Answer 5

Then it's not a zero~

Answer 6

is that what you got?

Answer 7

The roots are:
\[\LARGE x=0.23769, (-0.74384 \pm 1.2451i)\]

Answer 8

so that means there's no zeros right

Answer 9

@jim_thompson5910 @zzr0ck3r

Answer 10

If you sub x=-1 into the x portion of the function, you would notice that the function does not yield 0, thus x=-1 is not a 0

Answer 11

This is always the easiest way to check :)

Answer 12

Plug in x = -1 and evaluate

f(x) = -4x^3-5x^2-7x+2

f(-1) = -4(-1)^3-5(-1)^2-7(-1)+2

f(-1) = -4(-1)-5(1)-7(-1)+2

f(-1) = 4-5+7+2

f(-1) = 8

Since the result is NOT zero, this means that x = -1 is NOT a root (or zero) of f(x)

Answer 13

explain how each theorem can be used in determining the solutions for f(x)=x^3+4x^2-x-10

fundemental theorem of algebra and descartes rule of signs and rational root theorem
@jim_thompson5910