in-15-23-a-find-the-value-of-the-discriminant-and-determine-if-the-roots-of-the-quadratic-equation-4

Question

In $15-23 :$ a. Find the value of the discriminant and determine if the roots of the quadratic equation are $(1)$ rational and unequal, $(2)$ rational and equal, $(3)$ irrational and unequal, or $(4)$ not real numbers. b. Use any method to find the real roots of the equation if they exist. 
$$
2 x^{2}-8=0
$$

Alice . · Accepted Answer

for this equation, we&#x27;re going to try and find out more about it by taking the disc imminent. This permanent is B squared minus for a C. Is that part of the quadratic formula pratfalls underneath the square and knowing what the value of this is can tell us whether or not the roots are really repeated or uh, like imaginary. So let&#x27;s just calculated right now. So be is the coefficient on the X term. So since there&#x27;s no cowfish in there, we do zero over its and zero squared to zero minus four times two times eight would be equal to minus 64. And there&#x27;s money. 64 is less than zero. We know that there&#x27;s two imaginary roots actually, actually miscalculated that it&#x27;s minus eight. So B plus 64 which is great evidence here. So there&#x27;s two real roots. So since there&#x27;s two real roots, then using that information, we&#x27;re able to say we&#x27;re able to do, uh, at least take the square root of the discrimination to figure out whether they&#x27;re rational. Rio roots since 64 is a perfect square, it becomes out to eight. So when we closer minus it, we&#x27;re going to get rational numbers. So there&#x27;s two riel rational, unequal, rich. So if I was to solve this, I would probably just move the eight to the other side and then sold for X squared. So I get X squared is equal to four. And if I took the square root of four, you get two answers. You get minus two and two, and that makes sense according to what we calculated about the discriminate.

Alice . · Answer

The point of this problem is to use indiscriminate to learn more about the solutions to this quadratic equation. So we&#x27;ll use that discriminate, which is the part of the quadratic formula that falls under the square root, which is B squared minus for a C. So be here is minus three, so it&#x27;s minus three squared minus for a seat, so it&#x27;s four times two times minus five is equal to the discriminating. So we get that it&#x27;s nine minus eight times minus five would be 40. Toby plus 40 equals 49. And since we know that 40 that is greater than zero, there&#x27;s gonna be two real roots. We&#x27;ll finish it. Zero. And so let&#x27;s take the square root of 49 only find that seven. And since it&#x27;s a perfect spirit that we know that the two real roots are gonna be rational, but we have tube real rational Ruth and we know that are also gonna be unequal because there is value be in this, and also it&#x27;s not equal to zero. D&#x27;oh, I&#x27;m discriminated. So if we keep going, I think the best way to solve this is probably factoring. So it&#x27;s due to x x five one and then we put in tthe e meg. Do so would be minus five and plus ones Cool t zero and little for X. So we get five hives and minus one as spirits and those are the solutions, so they&#x27;re real, unequal and rational.

Sanchit Gogia · Answer

given the equation. X square minus 12 X plus 36. They could see well, we could find Indiscriminant isn&#x27;t 12 minus Always be 26 s e, and one is a so discriminating T physical too minus 12 square minus for one 26 with foot on me. 1 44 minus 1 44 The physical Xerox. So that means the roots of this equation far equal. So that means, is the perfect swear we were in the equation. We can see that X square minus two six X plus six square just turned out to be an identity which is a menace to be square so we can rewrite this hours X minus six cools where or X minus sex x minus sex so that two routes of the equation are sex, comma sex.

Alice . · Answer

so on this problem, we&#x27;re gonna use discriminative first to you find out more information about this quadratic equation. So the discriminative going to B B squared minus four e c. Which is like the middle off, the scary in the quadratic equation. Our car drug formula. Ah, solution. So if the experiments created and zero, we know that there&#x27;s two real roots. Um, so let&#x27;s just let&#x27;s just all for it right now. And if we know that is equal to zero, we know there&#x27;s a repeated route. We know that it&#x27;s less than zero. There&#x27;s gonna be imaginary bits. So, uh, b squared here is 49 minus ah four times a, which is two times C, which is zero. And that&#x27;s equal to 49 because 49 is, ah, greater than zero. We know that there&#x27;s two real roots. We also know that the square root of 49 is equal to seven. So on top of nine of those two routes, there are two riel rational and unequal roots. Probably the best way to solve this would be factory. So if I factor on X term from this equation, I&#x27;ll get two x plus seven and solving this quarter equation. I get that X can be zero and it can be minus seven over too. And those are my two solutions.

Sanchit Gogia · Answer

can. The equation for X clear minus X is equal to one. We can revitalise us for X square, minus X minus one for the disk women int we use minus one is B. My eyes want to see, and four is a that would be minus one square miles, four minus for is that one. So that would become one plus 16 which is 17. So since this is quitted and zero, but it&#x27;s not a perfect square, it will fall into number three category that is irrational and not e quo, not fund the votes. We can use the quadratic formula that isn&#x27;t minus B plus minus. It&#x27;s weird 50 as terminal point to a, which would then be one plus minus word of 17 upon Hey, and that comes X is equal to one plus Route 17.8 or one minus 17 upon eight

Sanchit Gogia · Answer

you&#x27;re in the equation. Ex Clearer plus three X plus von Z equals zero. You can find the discrimination using peace where minus four a. C. This year would be three skirt minus four one one, which is mine minus four. This is equal to five. Since the is equal to five. We can say that the boots here are irrational and on equal, so that corresponds to Number three. Now to find the lute&#x27;s, we can use the cooperating formula that we learn that as minus B plus minus one day upon to a that should be minus three plus minus. It&#x27;s clear of five upon to a they said they minus three plus flute five upon two comma minus twe minus with five divided by two.

Problem

In $15-23 :$ a. Find the value of the discriminan…

Problem 18 Easy Difficulty

Answer

(a) Discriminant $=(-8)^{2}-4(2)(0)=64$
The discriminant is a perfect square number so the roots of the equation are: (1) rational and unequal
(b) The roots are $x=0,4$

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Ann Xavier Gantert

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Heather Z.

Alayna H.

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Kristen K.

Absolute Value - Example 1

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(a) Discriminant $=(-8)^{2}-4(2)(0)=64$The discriminant is a perfect square number so the roots of the equation are: (1) rational and unequal(b) The roots are $x=0,4$

Algebra 2 and Trigonometry

Heather Z.

Alayna H.

Kayleah T.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Heather Z.

Alayna H.

Kayleah T.

Kristen K.

(a) Discriminant $=(-8)^{2}-4(2)(0)=64$
The discriminant is a perfect square number so the roots of the equation are: (1) rational and unequal
(b) The roots are $x=0,4$

Ann Xavier Gantert

Algebra 2 and Trigonometry