in-3-14-use-the-quadratic-formula-to-find-the-roots-of-each-equation-irrational-roots-should-be-w-12

Question

In $3-14$ , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form. 
$$
2 x^{2}=x+4
$$

Bahar Tehranipoor · Accepted Answer

in this exercise, we want to use the quadratic formula to find our roots. So first wait to get into the form of a X squared plus bx C to use our formula. So if we subtract execrable sides to track for, both sides will get theirs. We have two X squared minus X minus four equals zero and now they can use our quadratic formula. And that would be opposite Be a plus or minus squared of B squared minus for a C over to a Let&#x27;s begin. So negative b is going to be negative. Negative one. So we have one plus or minus the square root of B squared, which is going to be negative. One squared one minus four times A, which is two times C, which is negative for over two. A where a. Here&#x27;s two, so two times two is four. Let&#x27;s simplify with Insider Square. Here you have one minus four times two times before, which is the same as one plus four times, two times four. So four times he has 88 times four is 32. This equals 33 so we can rewrite this as one plus or minus the square root of 33 over four. So we can&#x27;t actually simplify this square anymore. Because 33 is just three times 11. Those are both prime, so there&#x27;s there&#x27;s no way to score there. You can rewrite our roots as one plus the square root of 33 over four and one minus squared of 33 over four. Those are our roots.

Bahar Tehranipoor · Answer

in this exercise, we want to use the quadratic formula. So we have to kind of move some stuff around in this equation that we have here to able to do that because we use equation for the formula, we have a X squared plus BX plus C. Then we can use our formula on this. So if we just subtract four from both sides, we have to have it equal to zero struck. Horrible size. We get X squared plus two x minus four equals zero. Now we can use the quadratic formula so we have opposite be a plus or minus the square root of B squared minus for a C over to a plug. Everything at so be is too. Here&#x27;s we have negative too. Plus or minus the square root of two squared just four minus four times A, which is one times C, which is negative for over two A. Where is one? So we have to. Then we can rewrite this So let&#x27;s first simplify What&#x27;s inside are radical. Here we have four minus four times. One has to get a force that&#x27;s just four plus four times for so 16 that equals 20 so we have that this actually equals negative to plus or minus the square root of 20 over too. But we can actually simplify square 20 because there&#x27;s a square of four and there&#x27;s we have four times five in here. If we take out the square before, which is to weaken, rewrite this as negative to plus or minus the square root of just two times the square of five over, too. And now let&#x27;s clean this up and write our individual roots. We divided to out we have negative one plus the square root of five for our first room because negative to over two is needed +12 or five over to Israel. Five. Excuse me. And our second room is just going to be the minus. Seriously. First it plus about minus. We have negative one minus the square root of five. And these are our tourists

Elizabeth Xu · Answer

in this question here. If we bring everything to one side, we get three X squared minus four X minus two is equal to zero. So as you can see here, our A Z three b is negative for and see is negative two. So you have negative B plus minus the square root of B squared minus four a. C divided by two a. Now this is equal before plus minus. Discourage a 40 departed by six What is equal to four plus minus two. Route 10 over six. And if if divide the numerator and denominator high factor too, you get too close. Finest Route 10 over three So you have two solutions here we have two plus wrote 10 divided by three in two minus root 10 divided by three

Bahar Tehranipoor · Answer

and this exercise, we want to use the quadratic formula to find over. It&#x27;s so formula says our roots are gonna be negative B plus or minus the square root of B squared minus right that over time B squared minus for a C over to a Let&#x27;s just plug that in so sick opposite. Beware be his negative ones. We have one plus or minus squared. So we have be square with his negative one squared just one minus four times A, which is one times C, which is negative for over two aces two times. Well, now we could just clean what&#x27;s inside here We have one minus four times, one times negative four, which is the same as saying one plus four times for so one plus 16 equals 17. So we have that this equals one plus or minus the squared of 17 over too. So our roots are going to be one plus the square root of 17 over too, and one minus the square root of 17 over, too. And those are our roots

Bahar Tehranipoor · Answer

in this exercise we want to solve for the routes using the quadratic formula. So to use the computer formula, it&#x27;s negative B plus or minus a squared B squared minus for a C over to a Let&#x27;s just play everything it so upset he is going to be negative. Negative ones. We have one plus or minus the square root of B squares from negative one square, just one minus four times a just four times seat, which is negative. One over to a so a. Here&#x27;s four, so two times four is eight. Let&#x27;s clean up with the side or square. Here we have one minus four times four times negative ones. That&#x27;s just one plus four times for just 16 in the sequels. 17. Now we can rewrite this as one plus or minus the square root of 17 over eight, and to rewrite our individual routes. We have one plus squared of 17 over eight, and it&#x27;s also used or minus. We have worn minus the square root of 17 over Kate, and those are our roots

Elizabeth Xu · Answer

quadratic formula to find this years. And he you question we have never to be were negative. Five plus minus quiver. Be square minus four times a time. See, divided by two. Okay, this is equal to negative. Five plus minus the square root off 25 minus 16 which is nine. Divided by two. This is it with negative five plus minus 3/2. So you have negative five plus 3/2, which is equal to negative one. And we also have negative five minus 3/2. Well, you see, go to negative four. So our solutions are accessing. Good. Tonight of one. An X is equal to negative for.

Problem

In $3-14$ , use the quadratic formula to find the…

Problem 14 Easy Difficulty

In $3-14$ , use the quadratic formula to find the roots of each equation. Irrational roots should be written in simplest radical form.
$$
2 x^{2}=x+4
$$

Answer

$\frac{1+\sqrt{33}}{4}$ and $\frac{1-\sqrt{33}}{4}$

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Algebra Educators

Catherine R.

Anna Marie V.

Kayleah T.

Michael J.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 5

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{1+\sqrt{33}}{4}$ and $\frac{1-\sqrt{33}}{4}$

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Kayleah T.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry