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  • - [Instructor] We're told we want to find the zeros

  • of this polynomial and they give us

  • the polynomial right over here, and it's in factored form.

  • And they say plot all the zeros,

  • or the x-intercepts, of the polynomial

  • in the interactive graph.

  • And so this is a screenshot from Khan Academy.

  • If you're doing it on Khan Academy,

  • you would click where the zeros are to plot the zeros,

  • but I'm just gonna draw it in.

  • So pause this video and see if you could have a go

  • at this before we work on this together.

  • All right, now let's work on this together.

  • So the zeros are the x values

  • that make our polynomial equal to zero.

  • So another way to think about it is

  • for what x values are p of x equal to zero?

  • Those would be the zeros.

  • So essentially, we have to say,

  • hey, what x values would make two x times two x

  • plus three times x minus two,

  • 'cause this is p of x, what x values would

  • make this equal to zero?

  • Well, as we've talked about in previous videos,

  • if you take the product of things and that equals zero,

  • if any one of those things equal zero,

  • at least one of those things equal zero,

  • make the whole product equal zero.

  • So for example, if two x is equal to zero,

  • it would make the whole thing zero,

  • so two x could be equal to zero,

  • and if two x is equal to zero,

  • that means x is equal to zero, and you could try that out.

  • If x is equal to zero, this part right over here is

  • going to be equal zero.

  • Doesn't matter what these other two things are.

  • Zero times something times something is

  • going to be equal to zero.

  • And then you could say,

  • well, well maybe two x plus three is equal to zero,

  • so we could just write that.

  • Two x plus three is equal to zero,

  • and if that were true, what would x, or what would x

  • have to be in order to make that true?

  • Subtract three from both sides,

  • two x would have to be equal to negative three,

  • or x would be equal to negative 3/2.

  • So this is another x value

  • that would make the whole thing zero,

  • 'cause if x is equal to negative 3/2, then two x plus three

  • is equal to zero, you take a zero times whatever this is

  • and whatever that is, you're gonna get zero.

  • And then last but not least,

  • x minus two could be equal to zero.

  • That would make the whole product equal to zero.

  • So what x value makes x minus two equal zero?

  • We'll add two to both sides,

  • and you would get x is equal to two.

  • If x equals two, that equals zero,

  • doesn't matter what these other two things are.

  • Zero times something times something is

  • going to be equal to zero.

  • So just like that, we have the zeros of our polynomial,

  • and the reason why they have

  • x-intercepts in parentheses here

  • is that's where the graph of p of x,

  • if you say y equals p of x,

  • that's where it would intersect the x-axis,

  • and that's because that's

  • where our polynomial is equal to zero.

  • So let's see, we have x equal zero

  • which is right over there.

  • Once again, if you're doing this on Khan Academy,

  • you would just click right over there

  • and it would put a little dot there.

  • We have x is equal to negative 3/2,

  • which is the same thing as negative 1/2,

  • so that's right over there.

  • And then, we have x equals two, which is right over there.

  • So those are the x-intercepts

  • or the zeros of that polynomial.

  • Now, this is useful in life,

  • because you could use it to graph a function.

  • I don't know exactly what this function looks like,

  • maybe it looks something like this,

  • maybe it looks something like this.

  • We would have to try out a few other values to get a sense

  • of that, but we at least know

  • where it's intersecting the x-axis.

  • It's at the zeros.

- [Instructor] We're told we want to find the zeros

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A2 初級

多項式のゼロ:ゼロのプロット|多項式グラフ|代数2|カーンアカデミー (Zeros of polynomials: plotting zeros | Polynomial graphs | Algebra 2 | Khan Academy)

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    林宜悉 に公開 2021 年 01 月 14 日
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