WEBVTT
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supposedly given upon a real P So p of X
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is a polynomial. And the question is, is
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there exactly one anti derivative anti which crosses the organs
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crossing origin? So it turns out that this is
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true on. We'll see why now. So it
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supposedly have a polynomial, and we take the anti
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derivatives. So just you notice like this particularly.
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Thank you. What we get is a different polynomial
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. Uh, and this polynomial has no constant term
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because what we've done is we've raised powers of X
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to take me on a derivative, and then we
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divide by than your parents. Uh, so we
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have this new polynomial, uh, plus C.
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And the idea here is that we can shoot,
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see in a specific way such that this anti derivative
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crosses the origin. So let's call this anti derivative
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capital P of X. So let's look at what
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happens at the origin me at the origin capital P
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at the origin is equal to. So when we
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plug in X equals zero into this polynomial over here
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, we remember that this polynomial has no cost in
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terms. So in this economy, we're just adding
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powers of X setting X equals zero shows us that
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this Ponyo zero at the origin. So what we're
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left with is PR zero is equal to the constant
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that we choose. Now. If we want our
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derivative across the origin, it must be that C
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equals zero. So what we have here is that
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there is exactly one choice of sea, which allows
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us to cross the Oregon, which means that there
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is exactly one anti derivative which crosses the origin.