adrien-said-that-if-the-roots-of-a-quadratic-equation-are-frac12-and-frac34-the-equation-is-4-x2-5-x

Name: adrien said that if the roots of a quadratic equation are frac12 and frac34 the equation is 4 x2 5 x
Uploaded: 2020-05-03
Duration: 1 min 49 s
Channel: Numerade
Description: Adrien said that if the roots of a quadratic equation are $\frac{1}{2}$ and $\frac{3}{4}$ , the equation is $4 x^{2}-5 x+\frac{3}{2}=0 .$ Olivia said that the equation is $8 x^{2}-10 x+3=0 .$ Who is correct? Justify your answer.

Question

Adrien said that if the roots of a quadratic equation are $\frac{1}{2}$ and $\frac{3}{4}$ , the equation is $4 x^{2}-5 x+\frac{3}{2}=0 .$ Olivia said that the equation is $8 x^{2}-10 x+3=0 .$ Who is correct? Justify your answer.

Zach Steedman · Accepted Answer

you have to. Students with two equations get to decide who is right. We&#x27;re gonna use the fact that Route one puts route two equals B over a in sake, 1/2 less three force. Excuse me and say, Well, 1/2 is equal to to force meaning? If I added these, it would be 5/4 so immediately. I&#x27;m thinking that this student might be right, because if this equals negative B over a, I see a negative five for a B value here, and I see a four for in a value. So let&#x27;s check if it works when I multiply these two. I have a 1/2 times of three. Fourth in this equals 3/8 which should be a C divided by a We&#x27;ll see value for this student is equal to 3/2. If I divide that by the A value of four well, that&#x27;s the same thing is saying, Why don&#x27;t we just say multiply by 1/4? And if I multiply by 1/4 check it out. I do get that 3/8 that we want. And so, yes, for sure, this student is right because of these two things checking out But this student is also right. And here&#x27;s why. If I take this equation and multiply everything by two, I get every single term. Here. Take a look. Two times for X where. Eight X squared two times negative five x negative 10 x into sensory over two is three Additionally, to times zero is zero. So, really, you can kind of say these two equations are exactly the same, with one having an a value equal to eight in another, having in a value equal to four. And so there&#x27;s different values kind of just affected the terms differently, but really, these both are the same equation with the same roots of 1/2 and 3/4.

Adnan Gill · Answer

so I am asked to find ah solution to this equation to X squared. Last four hex minus three is equal to zero. This is an equation contracting equation off the form he X squared plus BX plus C is equal to zero with a B equal to two be being equal to four and see being equal to negative three. So the easiest way to solve this equation is to form is to use something called the quadratic formula. So we have access equal to negative P that&#x27;s so minus the square root off P C B squared minus four A. C divided by two, eh? Once I have t quadratic formula, the next thing that I need to do is simply replace the letters by their appropriate numbers. So I&#x27;m going to substitute for a ah two for B four and foresee negative three. So I have X is equal to negative for lasso minus four squared minus four. See under the square root divide by two times a day, so X equals negative for so minus sixteen plus twenty four under the square. Root over four or X is equal to negative for lasso minus forty square root over four. Now this is where we need to pay a little bit more attention to what&#x27;s going on. So we have negative for last. So minus remember, forty equals four times ten. So I can write Square Goto, forty. Ask with the four times world of ten over four. So we got X is equal to negative for plus or minus two squared off ten over four. And what I can do here if I can factor too from D ah numerator. So I&#x27;m going to just factor to from the numerator that&#x27;s going to give me negative too. Lhasa Linus squared off ten over four and two over four simplifies to one over two, so I can now go ahead and write this as negative two plus or minus the square root off ten over two. And the correct answer, therefore would be option is so again what I did there. Wass used to quadratic formula substituting in the formula, is equal to basically before and C is equal to negative three

Ankit Gupta · Answer

we need to explain that who has all the problem correctly? That this Russian tortilla on the given equation is to X square minus eight. Dicks plus 10 equals to zero, and we have the solid by using completing the square. So Harry observed at the equation, is not in a perfect square. So for civil divide the equation by the coefficient of X square, that is too. So the question becomes X squared minus for X plus five equals to zero. No relight the equation such that the left side of the question is off the form X squared plus bx. So the question becomes X squared minus four. X equals two minus five. Now we observe that the left side of the question is not a perfect square. So first of all, make it into a perfect square for this divider. Confession off ex bite to minus four is divided by two. We get minus two now square This number after squaring you&#x27;ll get for now, aren&#x27;t for the both side of the equation. So the question becomes X squared minus four x plus four is equal to minus five. Bless for now. The left side of the equation is a Prophet Square, which is X minus two. Whole square is equal to minus one. From here, we&#x27;ll get X minus two equals two less minus underwrote minus one and underwrote minus one is iota. So we can write. X minus two is equals two plus minus LDA. From here, we&#x27;ll get the value of excess to bless. Minus Ida and the same little It was a plane by t also so ta is correct.

Sriram Soundarrajan · Answer

did it ever. Problem number. Think the given quarter a key question is Thanks, Claire. As through X plus three equals zero. No solution. No. We got off. Traditions will be because Baba, if highest applies toe terribly perforations for this. Well, whether that is yes, traditional, there&#x27;s or not. If one is a solution, every substance warning place off pecker. One squared plus two plus three is north recorder. That&#x27;ll soberness more desperation for this. But we can find whether we hardly your roof or imaginary worry quartered B squared minus four is it beef? This truth where? Minus four in DuPont, Into three for my Just do it. We just left them little B How this think imaginary roots for this increase. And you know that&#x27;s their tough A question. Thank you.

Meredith Moody · Answer

I can solve this quadratic equation by factory, but I&#x27;m not going to I&#x27;m gonna solve it using the quadratic formula and you may struggle with Remember there remembering the quadratic formula But if you do, I have really good news for you. I have a song that will help you remember the quadratic formula will ever and always and it&#x27;s got it sings Teoh are goes to the to her pop goes the weasel which is a traditional song so and I&#x27;m I&#x27;m not infringing on the kind of copyright here s o The quadratic formula is X equals negative B plus ser minus the square off B squared minus four a. C ah lo her to a You&#x27;re welcome. So now that we have the quadratic formula, all we have to do is identify our values and substitute them. So here my coefficient of my X squared is one. My coefficient of my B X turn is for and my coefficient of my C term is three. So now all I&#x27;m gonna do is I&#x27;m gonna substitute this in here So negative B plus or minus the square of B squared. My it is for a say what Ah, over Teoh A and then going Teoh simply do. Ah, my evaluation In here. So negative. Four plus or minus square root of foursquare to 16 minus four times one is four times three is 12 over. Two times one is two. Now I&#x27;m going. Teoh have negative four. That&#x27;s a little babbling for plus or minus. The square root of 16 minus 12 is four over. And you know what? I&#x27;m gonna move us over that letter to go down. I&#x27;ll just write smaller. So we have the square root of four now, Negative four plus or minus the square root of four, which is to over to. And we can do negative or plus two over to which is negative. 2/2. Which is? I remember I was just a little bit more. Just a teensy bit. There we go. Negative one. Or we can do negative for minus 2/2, which is negative. Six over two, which is negative. Great. So our solution is that X equals negative one or negative three. So our solution set is negative one and negative three. Which, by the way, if you factor this, that is what you get cause Just the funds these we get X Plus one and X plus three equals zero. So you get minus one and minus three. All right, you

Cory Kuzinski · Answer

X squared plus four X plus five. We&#x27;re solve this equation. We can do it any way we want. Um, I would initially look for factors of five that have before, but there are none. So it&#x27;s not fact herbal. So my next options it&#x27;s lead coefficient is one is that I&#x27;m gonna use completing the square. Oops. So we subtract five from both sides. Then what am I gonna add to both sides to complete the square? I&#x27;m gonna add four. Because half of this four is two and two squares for so even at affordable sides, that&#x27;s going to give me X Plus two squared equals negative one. And at this point, um, how can you square something and have, ah, negative number? You can&#x27;t so gonna stop right here and say there is no real numbers solution or no riel solution to this equation.

Problem

Without solving each equation, find the sum and p…

Problem 2 Medium Difficulty

Adrien said that if the roots of a quadratic equation are $\frac{1}{2}$ and $\frac{3}{4}$ , the equation is $4 x^{2}-5 x+\frac{3}{2}=0 .$ Olivia said that the equation is $8 x^{2}-10 x+3=0 .$ Who is correct? Justify your answer.

Answer

For $a=8$ the equation becomes
$8 x^{2}-10 x+3=0$ (Olivia)
and for $a=4$ it becomes
$4 x^{2}-5 x+\frac{3}{2}=0$ (Adrien)

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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For $a=8$ the equation becomes$8 x^{2}-10 x+3=0$ (Olivia)and for $a=4$ it becomes$4 x^{2}-5 x+\frac{3}{2}=0$ (Adrien)

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Kayleah T.

Kristen K.

For $a=8$ the equation becomes
$8 x^{2}-10 x+3=0$ (Olivia)
and for $a=4$ it becomes
$4 x^{2}-5 x+\frac{3}{2}=0$ (Adrien)

Ann Xavier Gantert

Algebra 2 and Trigonometry