Question

Decide whether the given x value is a zero of the function.

f(x) = x3 + 3x2 – 5x + 8; x = 4

Answer 1

a. No, because there is more than one zero .
b. No, because substituting the value does not balance the equation.
c. Yes, because substituting the value does balance the equation.
d. none of the above

Answer 2

Well a zero is a value such that when you plug it in, you output 0. That is you should check if f(4) = 0

Answer 3

I got a hundred. Would the answer b A?

Answer 4

@kirbykirby

Answer 5

well it's true that 4 is not a zero.. but you should check if there is more than one zero fr this problem (the reasoning for the "No" might not be correct... )

b) doesn't make sense what the reasoning is.. because you aren't verifying if anything is being balanced. You are plugging in a value for x and THEN checking what that output value is, but it's not a "verification" because you don't know the initial output you're checking

Answer 6

To check how many zeros your function has, you can check what the zeros are by solving for x:
\(0 = x^3 + 3x^2 – 5x + 8\)

Answer 7

Actually this is not such a nice function.. you could actually just graph it and see how many zeros you have: http://www.wolframalpha.com/input/?i=x3+%2B+3x2+%E2%80%93+5x+%2B+8

Answer 8

How do I find out how many zeros I have

Answer 9

well check how many times the graph crosses the x-axis (in the link I provided)

Answer 10

2 times?

Answer 11

it only crosses once (a bit to the left of -4 )

Answer 12

wait actually... have you seen complex numbers?

Answer 13

yes

Answer 14

Ah ok then.. actually it will have more than one zero if you consider complex roots (This is from the Fundamental Theorem of Algebra) , then

Answer 15

then A would be right

Answer 16

Okay. Thank you so much for your help!

Answer 17

=]

Answer 18

can you help me with some more?

Answer 19

ok

Answer 20

The Fundamental Theorem of Algebra helps to:

a. solve irrational equations
b. solve quadratic equations
c. solve linear equations
d. solve rational equations

Answer 21

can you select more than 1?

Answer 22

no I can't

Answer 23

well it's not a or d for sure.

Answer 24

I guess its more useful for a quadratic equation since linear equations are simple

Answer 25

okay thank you

Answer 26

what about this one

A root can be described as:

a. a solution to the base of leading coefficient
b. a solution to the equation
c. an answer to the inverse equation
d. none of the above

Answer 27

I feel like it's d.. the statement"a solution to the equation" is very vague. It could be a solution to the equation if you know the y-value .

Answer 28

Because a function is not technically an equation. It's more like a relation