Help w homework :sob: | Mathematics | Page 1

unkempt robin Jan 18, 2023, 7:44 PM

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4x^2 + 15x + 9 ≥ 0
Factor it first, then use the method of intervals.

gloomy badge Jan 18, 2023, 7:44 PM

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Add nine to both sides. Then solve it like you would a quadratic. So either factoring or quadratic formula

grizzled oriole Jan 18, 2023, 7:45 PM

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Yeah I always get confused with putting it into double brackers when theres like 2+x^2 not just x^2

grizzled oriole Jan 18, 2023, 9:04 PM

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Still need help turning it into double brackets ^^

unkempt robin Jan 18, 2023, 9:04 PM

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grizzled oriole Still need help turning it into double brackets ^^

What do you mean by "double brackets"?

grizzled oriole Jan 18, 2023, 9:06 PM

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So you turn it into something like
(4x+4)(x+6)

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And then X is either -4 or -6 which iss the answer to the question

unkempt robin Jan 18, 2023, 9:07 PM

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No, that would be the answer to an equation.

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Here you have an inequality.

grizzled oriole Jan 18, 2023, 9:07 PM

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Yeah it's like
x >/ -4
x >/ -6

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I think

unkempt robin Jan 18, 2023, 9:08 PM

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To factor 4x^2 + 15x + 9, solve 4x^2 + 15x + 9 = 0, getting roots x1 and x2. Then 4x^2 + 15x + 9 = 4(x - x1)(x - x2).

grizzled oriole Jan 18, 2023, 9:08 PM

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It's gotta be like
(amount of x - or + number) though

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It would be 1x or 2x for the second num in the brakcets

unkempt robin Jan 18, 2023, 9:09 PM

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I don't understand what you mean.

grizzled oriole Jan 18, 2023, 9:09 PM

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So like

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The answer has to be

(5x+5)(x+3)

Something like that, just changing the numbers

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Not like (5x+2x)(x+3)

unkempt robin Jan 18, 2023, 9:09 PM

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That's just the factorisation, not the answer yet.

grizzled oriole Jan 18, 2023, 9:09 PM

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Ik but idk how to work out the answer through that way 😭

unkempt robin Jan 18, 2023, 9:10 PM

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unkempt robin To factor 4x^2 + 15x + 9, solve 4x^2 + 15x + 9 = 0, getting roots x1 and x2. The...

Like this.

grizzled oriole Jan 18, 2023, 9:32 PM

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Yeah but with the method you used, I don't know how to work out the answer with that

unkempt robin Jan 18, 2023, 9:32 PM

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grizzled oriole Yeah but with the method you used, I don't know how to work out the answer with ...

Can you solve 4x^2 + 15x + 9 = 0?

grizzled oriole Jan 18, 2023, 9:33 PM

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Turning it into the double brackets is the part I'm strugglign with

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Once I do that, I can work out the answer

unkempt robin Jan 18, 2023, 9:34 PM

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grizzled oriole Turning it into the double brackets is the part I'm strugglign with

That is called "factoring". And the way to do it is solve the equation first.

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So, can you solve 4x^2 + 15x + 9 = 0?

grizzled oriole Jan 18, 2023, 9:34 PM

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unkempt robin That is called "factoring". And the way to do it is solve the equation first.

Idk but the thing I'm tryna do you turn it into brackets first, idk what you mean by solve

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I gotta turn it into like (4x+2)(x+6) first

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Then I can work out the answer

unkempt robin Jan 18, 2023, 9:36 PM

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grizzled oriole Idk but the thing I'm tryna do you turn it into brackets first, idk what you mea...

But that IS how you factor it!

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Fine, let me show.

grizzled oriole Jan 18, 2023, 9:36 PM

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Wdym??

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Idk what you mean by solve

unkempt robin Jan 18, 2023, 9:38 PM

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4x^2 + 15x + 9 = 0
Using the quadratic formula, we get:
x = (-15 ± √(15^2 - 4*9*4))/8 = (-15 ± √(81))/8 = (-15 ± 9)/8
So, the solutions are:
x = (-15 - 9)/8 = -3
x = (-15 + 9)/8 = -3/4
Thus, the factorisation is:
4x^2 + 15x + 9 = 4(x + 3)(x + 3/4)
And now you can solve the inequality.

grizzled oriole Jan 18, 2023, 9:39 PM

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I've never used that method

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I'm struggling with this I cant try learn other stuff too it'll be way too confusing

unkempt robin Jan 18, 2023, 9:39 PM

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Wait, but how did you factor quadratic polynomials before, then?

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This is the main method, after all.

grizzled oriole Jan 18, 2023, 9:42 PM

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quadratic polynomials ?

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ive never heard of that word before 😭

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I just need to put 4x^2 + 15x + 9 into double brackets then I can work it out

unkempt robin Jan 18, 2023, 9:44 PM

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What you're calling "putting in double brackets" is properly called "factoring".
And a quadratic polynomial is a function of the form ax^2 + bx + c.

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So, how did you factor them before, if not by finding the roots?

grizzled oriole Jan 18, 2023, 9:49 PM

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Wdym I just get this, and factorise it into double brackets, then the answer from there is simple

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I'd be able to do it but the 4x^2 confuses me, if it's normal x^2 i'm fine

grizzled oriole Jan 18, 2023, 10:07 PM

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grizzled oriole I'd be able to do it but the 4x^2 confuses me, if it's normal x^2 i'm fine

Then divide everything by four

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$4x^2 + 15x ≥ -9$
$\\frac{4x^2 + 15}{4} ≥ \frac{-9}{4}$
$\x^2 + \frac{15x}{4} ≥ \frac{-9}{4}$

mystic archBOT Jan 18, 2023, 10:09 PM

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Miguel

grizzled oriole Jan 18, 2023, 10:53 PM

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grizzled oriole Then divide everything by four

But 15 and 9 don't go into 4

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And how would you do it w decimals

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aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

grizzled oriole Jan 18, 2023, 11:04 PM

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grizzled oriole And how would you do it w decimals

Uhm

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Is $x^2 + 3.75x ≥ 2.25$ better?

mystic archBOT Jan 18, 2023, 11:05 PM

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Miguel

grizzled oriole Jan 18, 2023, 11:06 PM

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grizzled oriole Is $x^2 + 3.75x ≥ 2.25$ better?

uhh it's just
x > number

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and 2 dif values ^^

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i dont get this

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What don't you get?

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what the hell do i do with that 😭 🤣

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Well you said that you knew how to solve it if the x² didn't have anything before it, didn't you?

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You basically have to add 2.25 in both sides and factorise

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$x^2 + 3.75x + 2.25 ≥ -2.25 + 2.25\(x+3)(x+0.75) ≥ 0$

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And you should know how to continue from here

mystic archBOT Jan 18, 2023, 11:36 PM

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Miguel

radiant plume Jan 18, 2023, 11:38 PM

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@grizzled oriole I'm gonna teach you something new. I know you said you don't want to learn anything new, but if you can't solve this with what you already know then you need to learn something new to be able to do it.

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It's called "slide and divide".

#Help w homework :sob: