Using the Intermediate Value Theorem and a calculator, find an interval of length 0.01 that contains a root of x 5 − x 2 + 2 x + 3 = 0, rounding off interval endpoints to the nearest hundredth.I've done a few things like entering values into the given equation until I get two values who are 0.01 apart and results are negative and positive ( − 1.15 &amp; − 1.16), but these answers were incorrect.I'm at the point where I'm thinking there is not enough information to solve. Any ideas?

Question

Using the Intermediate Value Theorem and a calculator, find an interval of length 0.01 that contains a root of       x    5    −      x    2    +  2  x  +  3  =  0, rounding off interval endpoints to the nearest hundredth.I&#039;ve done a few things like entering values into the given equation until I get two values who are 0.01 apart and results are negative and positive (  −  1.15 &amp;amp;   −  1.16), but these answers were incorrect.I&#039;m at the point where I&#039;m thinking there is not enough information to solve. Any ideas?

humbast2 · Accepted Answer

f  (  x  )  =      x    5    −      x    2    +  2  x  +  3As you can see   f  (  0  )  =  3  &amp;gt;  0 and   f  (  −  1  )  =  −  1  &amp;lt;  0Thus there is at least one root of   f  (  x  )  =  0 in Interval   (  −  1  ,  0  )Now calculate the value of  f  (  −      1    2    )  =      55    32    &amp;gt;  0Thus now our interval is shortened and it is   (  −  1  ,  −      1    2    )  f  (  −      3    4    )  =      717    1024    &amp;gt;  0Our interval is now   (  −  1  ,  −      3    4    )  f  (  −      7    8    )  =  −      935    32768    &amp;lt;  0Our interval is now   (  −      7    8    ,  −      3    4    )similarly, keep doing until you get the desired result

Using the Intermediate Value Theorem and a calculator, find an interval of length 0.01 that...

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