Question

Between what two successive integers does a real zero of P(x) = x3 –2x –5 lie?

what are successive integers?

Answer 1

successive integers are integers that follow each other.

e.g. 4 and 5 are successive integers, 18 and 19 are successive integers, etc

Answer 2

you can find the zeros of \(P(x)\), and find the integers from that value...
for example if you find the real zero to be \(x=1.32\) then you know it lies between \(1\) and \(2\) ---( This is not the solution, i just made up an example ! )

Answer 3

Hey, let \(f(x) = x^3 - 2x - 5\).

Notice that \(f(2) = -1\) and \(f(3) = 16\). Therefore a root lies in the interval (2,3).

Answer 4

@Greg_D thanks. so all i have to do is find the zero and did whatever it's between is the answer?

Answer 5

yes!
remmeber your answer must be integer numbers!

Answer 6

oh ok. it is between 2 and 3 like parthkohli said. i also must use calculator. Thanks for the help!

Answer 7

Here, I used the Intermediate Value Theorem. There's no real need for a calculator although you can graph the function.

Answer 8

:) you are welcome!
@ParthKohli showed a more efficient way to solve this, without finding the value of the zero !

Answer 9

you don't need to actually work out the roots of this equation first.

Answer 10

you need to try successive integers until you observe a sign change - Intermediate Value Theorem as @ParthKohli stated