rita-said-that-when-the-product-of-three-linear-factors-is-greater-than-zero-all-of-the-factors-must

Name: rita said that when the product of three linear factors is greater than zero all of the factors must
Uploaded: 2019-11-23
Duration: 1 min 8 s
Channel: Numerade
Description: Rita said that when the product of three linear factors is greater than zero, all of the factors must be greater than zero or all of the factors must be less than zero. Do you agree with Rita? Explain why or why not.

Question

Rita said that when the product of three linear factors is greater than zero, all of the factors must be greater than zero or all of the factors must be less than zero. Do you agree with Rita? Explain why or why not.

Bahar Tehranipoor · Accepted Answer

in this exercise. We have this scenario where Rita says that the product of three linear factors has to be either greater than zero or all the must be, um, less than zero for the product to be positive. So do we agree with the statement? Explain why or why not? So basically, she&#x27;s trying to say You have these. Three numbers were just called X Y and Z and the X Y and Z will be greater than zero on Lee if all three of these are greater than zero or if all of them are less than zero. But we could actually really quickly conclude that if all three of these lessons and zero, we&#x27;re gonna have a negative times negative times negative and these two negatives will make a positive. But then we&#x27;ll still have a negative, which will lead eventually into a negative. So this is definitely not right. So we can already say that Rita is wrong, because that scenario does not provide us with the negative zero. The one thing that might be true is if we had a negative times a negative times a positive that would give us of the network and zero for the scenario that is described here. Rita is not correct.

Bahar Tehranipoor · Answer

in this exercise, we have that X corpse, be ecstasy is a polynomial and that this person, Rita, is saying that we only have real roots when B squared is greater than or equal to four a. C. And so this is a true statement. We agree with what Rita is saying because we&#x27;re doing the quadratic formula and we have opposite B plus or minus the square root of B squared minus for a seat over to a That&#x27;s our route. So when we have the script on this for a C for this route to be riel, this has to be greater than equal zero. So you could say B squared minus for a C Square than or equal zero and tow ad for a suitable sides we end up at B squared is greater than or equal to four a. C. So if this is true, it means that our roots are riel. So it Rita saying, is indeed correct

M S · Answer

So Shelly said, that exploit us five times X minus seven is less saying zero. So she said that Ex Money seven must be the negative factors, so it&#x27;s less than zero. And then she said that X minus by must be the positive factor. So X minus five must be good with zero with this a positive factor. So whatever we have inequalities or something for any qualities, we know that you&#x27;re gonna have to possible solutions. So in this case list, Stan means negative. Luna. Write that down, listing zero beings negative and to get a negative products, we must have a positive times the negatives. But we have to backers here, so we need to software the other possibility to that. This one is native and this one is positive. But I will also give us a negative negative product furnace case. Shelley says that X minus seven. It&#x27;s negative and explosive. Five is positive. So she&#x27;s going with the second possible solution here. Let&#x27;s just hope for it. So we have excess. Listen. Seven. Well, it&#x27;s a little far you next year that bought the boat. Sleds X is greater than father, so when it&#x27;s gonna bind these two so that we can have one statement. So how far here in seven years X is greater than fire? So to go that way and exploitable seven. So to go that way. And the common area between the two is here, they&#x27;re here. We know that the solution is correct and who could solve for the first possibility, But we would know that it is incorrect. So yes, Shelly is correct because when you saw, you can find which is a positive factor in which is a negative back there as we just failed, we also know that explain a spot cannot be negative. So excellent. A seven has been linked to factor because we switched on. We would not get a common area between the two because the signs will be put one part beat. It wants to know that Can we always tell which is the positive factor in which is the negative factor? My answer is no. Let&#x27;s say, for example, we have a So I&#x27;m speed, you know, give us native to you can&#x27;t prove which is negative. They could be negative or me to be negative. No, Both give us a negative answer. But we just cannot prove which back there is negative in this case

Rebecca Polasek · Answer

Sharon&#x27;s. And if F of X is a polynomial and f of a equals zero, then a is a root of the function. So the question is, Do we agree with Sharon? If F of X is some polynomial function and f A equals zero? Well, by definition, the number A is a zero of the Paul folk polynomial function if and only if f of a equals zero. So when you see the word route, you&#x27;re thinking of a couple different things. That&#x27;s the same thing, a solution. And it&#x27;s the same thing as zero. And by definition A is a route. It&#x27;s a solution. It zero if half of a equals is your oh so yes, Sharon is correct. She was actually going based on that definition, and that&#x27;s how you can find a route, a solution. The function is by whenever it&#x27;s equal to zero

Rebecca Polasek · Answer

for the polynomial function f of X. We know that our serve one are set to and arson. Three are the roots of the function. So the zeros, the solutions of the function we want to know. Then what are the roots of g of X if it is f of X minus A. So Jordan thinks that the routes should be our someone plus a arson two plus a and arson three plus a. The question is, do we agree with that? Well, by definition, if our simple 12 and three are roots of effort backs and we know that&#x27;s a moment where F goes to zero, so for ourselves, one are set to and our sub three f of X goes to zero. That&#x27;s the definition of the fact that they are roots of the original function. So I would recommend if Jordan thinks these air the roots over here. Fergie, how about we plug them in and then see what happens? So we fill these into G geo of our sub one plus a that&#x27;s going to get filled in tow, af but notice you only replace the x part of it. So I&#x27;m gonna have f of ours of one plus a I&#x27;m replacing this X, which means I didn&#x27;t replace the minus a Well, then, if I simplify plus a minus A is gonna cancel out And I know f of our sub one equals zero. So yeah, our sub one plus a when I put it into the function G does give me a root does give me zero And the same things that happened when I tried the other two Because we see that the plus a minus a So when I fill in tow axe I can&#x27;t feel into this minus a from the function So the plus a minus say every time&#x27;s gonna cross out and then you&#x27;re left with what you already know is a zero. So yes, each of these terms dyes work as a zero for the function G of X.

Tani Iqbal · Answer

So we&#x27;re going to look at the true or false problem, and it&#x27;s talking about a product of real number. So those numbers were going to call A and B, and they&#x27;re real numbers. The product of them is a times B or A B. And you said that equal to zero. This is true. Based on the statement, it says this is true if, and only if every factor. So it is equal to zero, so a s to be called a zero and B is equal to zero. So the way I&#x27;m going to prove this right or wrong is if, well, I think it&#x27;s false. And I want to do that through a couch, for example. So the counter example is, let&#x27;s say a is not equal to zero. So then a times be, but B is equal. Is there is equal to, Let&#x27;s see, a time zero eight times zero is equal to zero. So this doesn&#x27;t this necessarily true on Lee, one of them House of equal to Zero

Problem

Shelley said that if $(x-7)(x-5)<0,$ then $(x-7)$…

Problem 1 Easy Difficulty

Rita said that when the product of three linear factors is greater than zero, all of the factors must be greater than zero or all of the factors must be less than zero. Do you agree with Rita? Explain why or why not.

Answer

Rita was wrong because even if only one factor is greater than zero and the two others are both negative, the product of the three factors would still be positive.

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Rita was wrong because even if only one factor is greater than zero and the two others are both negative, the product of the three factors would still be positive.

Algebra 2 and Trigonometry

Grace H.

Heather Z.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Heather Z.

Caleb E.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry