Confusion with instruction - "Locate a zero of the function

[Nathalie]

Confusion with instruction. The instruction is "Locate a zero of the function between two consecutive integers".
My problem is
f(x) = x^2 - x - 3

So, I used quadratic formula and got the answer (1 - SQ RT of 13) / -6 and (1 + SQ RT of 13) / -6
But those two answers aren't between two consecutive integers...

I remember we were taught "Location Theorem", I am not sure if this is what I am supposed to do with this problem or not...
What exactly is the instruction asking?

Please help. Thanks in advance.

 

[mmm4444bot]

f(x) = x^2 - x - 3

… I used quadratic formula and got the [solutions x = ] (1 - SQ RT of 13) / -6

[or x = ] (1 + SQ RT of 13) / -6



I think that the zeros for f are:

x = [1 + sqrt(13)]/2

or

x = [1 - sqrt(13)]/2

Decimal approximations for these are x = -1.3 or x = 2.3; the former lies between the Integers -2 and -1, and the latter lies between the Integers 2 and 3.

So, either of these zeros satisfies the given instruction, but I'm not 100% sure what this exercise expects you to show.

 

[Nathalie]

Oh. It is 2a... I made a mistake. I wrote down 2ac.
Thanks~!

I am confused because the next question, under the same instruction is
f(x) = x^3 - 4x^2 + 5
I wonder if we are supposed to look up cubic formula to solve that problem or not. So yeah :/
Anyways, thanks a lot.

 

[mmm4444bot]

… f(x) = x^3 - 4x^2 + 5

I wonder if we are supposed to look up cubic formula to solve that problem …

I don't think so; the Cubic Formula is relatively more difficult.

I think that you're supposed to list the possible Rational zeros of f using the Rational Root Theorem. (There are only four possible Rational zeros, that come out of this theorem.)

Test these possibilities, one by one, until you find a zero (I'll represent this zero with the symbol c).

Divide the cubic by the factor (x - c), to get a quadratic quotient.

Use the Quadratic Formula to find the zeros of the quadratic factor.

 

[Denis]

x^3 - 4x^2 + 5 = (x + 1)(x^2 - 5x + 5)

 

[Nathalie]

Oooh! That works.

Thank you again.

 

[mmm4444bot]

That works.

Not always, I claim (based on my interpretation of your unreferenced pronoun).

Perhaps, the Wizard can explain what consecutive Integers have to do with this problem. That would be useful.

September quota met. When does October start?

 

[Denis]

Re:

Perhaps, the Wizard can explain what consecutive Integers have to do with this problem.

The Whizzerd simply factored x^3 - 4x^2 + 5 (in order to ride into the sunset with Fair Damsel Nathalie),
letting those left behind worry about the elusive Location Theorem (beneath yours truly's dignity!)

For anybody losing sleep about the aforetyped theorem, may I direct youze here:
http://www.google.ca/search?hl=en&sourc ... q=null&oq=