I don't get a step with this quadratic question

[Nathi ORea]

Homework Statement

I did the example, and actually got the same answer (0.215), but am a little confused how they did it.

So I did ; 16 - 4 x 5 x -1 = 28.

Then they factorise it into 4 x 7 for some reason.... then I have no idea what wizardry they perform on the next line.

Relevant Equations

Appreciate any help.

 

[Frabjous]

Are you familiar with the quadratic formula?
https://en.wikipedia.org/wiki/Quadratic_formula

 

[Nathi ORea]

Yup. So I used b2 - 4ac to find 28. All good. but I am not sure why they factorised 28?

 

[Frabjous]

Yup. So I used b2 - 4ac to find 28. All good. but I am not sure why they factorised 28?

Because they know they are about to take the square root and will want to bring the two outside of it. They are being overly descriptive.

 

[Nathi ORea]

What rule says you can bring the 2 outside of it?

 

[Frabjous]

$\sqrt{ab}=\sqrt{a} \sqrt{b}$

 

[Nathi ORea]

Oh. I see. I haven't got to that section yet. Thank you!

 

[Frabjous]

Oh. I see. I haven't got to that section yet. Thank you!

They are probably assuming that you already know this (i.e., there is not a section coming) so you will probably want to review this on your own.

 

[Mark44]

So I did ; 16 - 4 x 5 x -1 = 28.

Typo in your work. The above should be $16 - 4(3)(-1) = 28$.

So I used b2 - 4ac to find 28.

You've been a member here for almost three years. Please take the time to learn at least the rudiments of how to write mathematical expressions. At the very least, b^2 - 4ac. Better yet, using LaTeX to write $b^2 - 4ac$. When you're creating a post, there's a link to our LaTeX tutorial in the lower left corner.

 

[WWGD]

As Mark suggested, just wrap the expression b^2-4ac with ## tags for a start.

 

[PeroK]

Oh. I see. I haven't got to that section yet. Thank you!

It's a convention to take any square factors out of a square root. For example, if you ended up with $\sqrt 4$, that wouldn't be wrong in itself. But, the convention is to write that as $\sqrt 4 = 2$.

And, if you have $\sqrt{28}$, then again you are expected to look for square factors. In this case, $28$ has a factor of $4$. So, you are expected to write $\sqrt{28} = 2\sqrt 7$.

Note that some mathematicians take this sort of thing very seriously indeed and that leaving something as $\sqrt{28}$ ought to be punishable by a jail term. I don't see that it matters much, but perhaps that's why I'm not a mathematician.

 

[Nathi ORea]

It's a convention to take any square factors out of a square root. For example, if you ended up with $\sqrt 4$, that wouldn't be wrong in itself. But, the convention is to write that as $\sqrt 4 = 2$.

And, if you have $\sqrt{28}$, then again you are expected to look for square factors. In this case, $28$ has a factor of $4$. So, you are expected to write $\sqrt{28} = 2\sqrt 7$.

Note that some mathematicians take this sort of thing very seriously indeed and that leaving something as $\sqrt{28}$ ought to be punishable by a jail term. I don't see that it matters much, but perhaps that's why I'm not a mathematician.

Ahhhh.. so that’s why they did it! Thank you very much

 

[gmax137]

It's a convention to take any square factors out of a square root. For example, if you ended up with $\sqrt 4$, that wouldn't be wrong in itself. But, the convention is to write that as $\sqrt 4 = 2$.

And, if you have $\sqrt{28}$, then again you are expected to look for square factors. In this case, $28$ has a factor of $4$. So, you are expected to write $\sqrt{28} = 2\sqrt 7$.

Note that some mathematicians take this sort of thing very seriously indeed and that leaving something as $\sqrt{28}$ ought to be punishable by a jail term. I don't see that it matters much, but perhaps that's why I'm not a mathematician.

If one is looking for a numeric result, ie, a decimal answer (such as the 0.215 quoted in the OP), today you simply punch "SQRT 28" into your hand calculator and move on. That's actually fewer keys pressed than "2 times SQRT 7". In the old days, I think algebra lessons stopped at $2\sqrt 7$. Maybe because evaluating $\sqrt 7$ was an exercise in table lookups, or log tables, or slide rules; and these were topics/skills mastered prior to algebra.