sketch-the-graph-of-a-fifth-degree-polynomial-function-whose-leading-coefficient-is-positive-and-t-2

Name: sketch the graph of a fifth degree polynomial function whose leading coefficient is positive and t 2
Uploaded: 2019-03-28
Duration: 33 s
Channel: Numerade
Description: Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and that has a zero at $x=3$ of multiplicity 2 .

Question

Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and that has a zero at $x=3$ of multiplicity 2 .

Frank Lin · Accepted Answer

So this problem one started once. We want the fifty three Pelino leading Colombian positive. Ciro at X equals three with some university too. So we want something. This Andi wanted three people, five and hostage leading coefficient, actually, on something like this, they&#x27;re saying example that satisfy that condition.

Heather Zimmers · Answer

in this problem, we&#x27;re going to sketch the graph of a function that has these characteristics a negative leading coefficient, an AA degree and three real roots. Whenever you have an odd degree, polynomial Theo, end behavior is one end up and one in down. And if the leading coefficient is negative, it will be like a line with a negative slope where you have this end up and that end down. So as X goes to negative infinity, you&#x27;re going up on his ex Costa positive infinity, You&#x27;re going down. So we need this to have three real roots. That means three X intercept CE because every real root gives you an X intercept. So when you draw it, you could do something like what I&#x27;ve already sketched, which has three ex intercepts and you&#x27;ll have an example of what they&#x27;re looking for

Donald Albin · Answer

it appears that we&#x27;ve got a lot to dio in this question. But first I noticed that I have acts Times act something with X in it to the second power. So if I multiply, there&#x27;s all out. I know that I&#x27;m going to get X to the third power. So the degree is three because X to the third power. Um, the zeros we have to set either X equals zero or X minus three to the second power equal zero. Well, if X minus three to the second power equals zero, then, um, X minus three equals us. I&#x27;m just gonna erased the second power there. All right, if I solve the 2nd 1 I just add three on both sides and I get X equals three. Now the X equals zero zero has a multiplicity of one, and the X equals 30 because of this exponents, too, as a multiplicity of two. That means it&#x27;s going to kiss the x axis and turn around. Um, so this is gonna turn around. You have to write that down. You could write kiss. If you want to go and this is going to cross or go through, that&#x27;s supposed to say cross. Okay, now we&#x27;re just supposed to sketch it. So I have a point at X equals zero. I have a point at X equals three. I do need to think about the end behavior. And I see if I were to multiply that out, that the first term would be one X to the third power. That means that the leading coefficient is positive. So I&#x27;m gonna draw arrows. Leading coefficient is positive and that it&#x27;s an odd function. All right, so we&#x27;re going to cross zero, and then we&#x27;re gonna turn around at three. So we just crossed through zero, turn around at three. Now, we could use knowledge of the Y intercept to show.

Sara Sasani · Answer

In this video, he escapes the graph off for union. With the appalling description, zeros are X equal to minus three, minus 1/2 1/2 and to even be green and positive. Leading coefficients we called pulling a milk your place on because of zeros are called X equals minus three minus 1/2 1/2. And to the NPR minus three is a call to Tokyo but minus one over trees. To call Tokyo off one over to the car is equal to zero, which means that they crap off. P of X meets the X axis at four point X equal to minus three X equal to minus 1/2 extra quarter one were to accept what over? Because the degree of this polynomial is either and their leading coefficient is positive for the lift on right behavior off your ex. They haven&#x27;t X course to minus impunity. Tee off X increases of the tower pound on been exposed to plus infinity again. Topics increases because pound now let&#x27;s their escape photograph to escape. Photograph the chance not from the left side off the smallest little or from the right side off the largest. Let&#x27;s start from the left side off this month. Still on me. You start from the, uh, top off the eggs access because P of X close to plus infinity. So they start from here not below the exact since we start from the above Off the x axis eso we start from here and the draft needs to meet this point this point this point at this point. So they start from here past the point minus three and zero. And we have a turning point here toward Tu minus 1/2 and zero and they pass this point another turning point, and meet the point minus. Started a point of 1/2 and zero on another turning point and meet the point toe and zero. And the graph off your face course two plus and anything as exposed to last. Therefore, the graph would be something similar to these. And please note back. The solution to this question is not unit. I hope you enjoy watching this video and hang score budget

Donald Albin · Answer

All right, we have a function. And I would tell you that my answer for 39 is in a little more detail than the answer for this problem. Number 41. Um, nevertheless, if we want to find the degree, um, all we have to do is add up the exponents. So the degree is three plus two, which is five. The zeroes according to zero product property either X minus one equal zero or X plus two equals zero. So are zeros that we solve. Those two equations are at one and negative to one. And negative too. Now, the one zero that is one of the expert on that is three. So its multiplicity is three. I&#x27;m gonna write. The multiplicity is down here. This one is three. And the 2nd 1 here, the exponents to explain it is too. So the multiplicity is too. That means that three, the zero that has a multiplicity of three is going to cross through. It&#x27;s also going to be in a inflection point. So it&#x27;s gonna cross ups. I should write that in blue. Get back here. Going across with inflection. OK? The other one is going to kiss the X axis and turn around. So I was gonna write Turn. All right, So, um, are zeros are at one and negative too. It&#x27;s, ah, one of them. That negative too. The other one is at one. No, I know, because if I multiply this thing altogether, my, uh, leading term is going to be one x to the fifth power. Um, X, 1/3 power times extra Second power is X to the fifth power. So my leading term is one x to the fifth power. Be a five. We try that again. Oh, I hate it when I do that. Okay, one x to the fifth power. So the one is positive, and the five is odd. And so we&#x27;re going to see that the graph goes down and up. That&#x27;s what positive odd looks like. Okay, so when we hit the red point, we&#x27;re gonna turn around. Ah, just kiss the x axis and turn around. Now, when we go to the blue point, we&#x27;re actually gonna chew some inflection as it crosses. So it&#x27;s gonna go like this, change curvature and go back up again. So it did cross through, but it didn&#x27;t cross like straight through. Let me just show you what straight through would look like. I&#x27;m running out of colors, though that would be straight through. But instead we see some inflection. So it goes up and occurs and it goes the other way. Inflection. Um, so there is a

Ankit Gupta · Answer

we have to explain. It is possible or not. That is the degree of the paranormal should before And the real zeros are three number and opposed to leading coefficient that wins. It is like this. So see the degree that is four and three little. So that means here this will be if any of the videos are coinciding. So I can stake excess square so x square and see the value. It has only X minus one and x here. I can say that this is where you X plus one. So see, this would be like this when I put on this here. This is a graph people. And so the zeros will be here. Here, this is a little and your cr minus one plus one. So this is minus one and lit it up plus one. So this will be like this. So this would be like this when we goes up. This is left. It is including when he goes right. It is also increasing. So this is the required for normal? Yes. It is possible

Frank Lin · Answer

Okay, let&#x27;s put all these clues together so we can sketch a polynomial that meets all these requirements. If it&#x27;s 1/5 degree polynomial with the positive leading coefficient than its end, behavior is like this. So it could mean that the graph has five X intercepts or maybe three or maybe one. But it has to have that in behavior. Also, we know that it has a zero at X equals three, and it has a multiplicity of two. That means it&#x27;s a double zero. We get X equals three twice, and when that happens, it just goes down and touches and comes back so it could look something like this. There are lots of other possibilities, but that&#x27;s just one possibility.

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Problem 131 Easy Difficulty

Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and that has a zero at $x=3$ of multiplicity 2 .

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