Help with using theoroms ?

Use the upper and lower bound theorem find the smallest positive integer and largest negative integer that are upper and lower bounds , respectively for the real zeros of (B ) Approximate the real zeros of each polynomial to two P(x) decimal places .

P(x) = x ^ 4 - x ^ 3 - 8x ^ 2 - 12x - 25

1 Answer

  • 1 month ago

    Because the theorem is usually presented with synthetic division, which I hate, I'm going to take a different approach to approximating the real zeros.

    A rudimentary sketch will show that the real zeros are near -2 and +4.  Then you can use Newton's method to find out that they are nearer -2.29 and 4.07.

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