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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

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