Discussion between lab bhattacharjee and Cherry_Developer

11:17 AM

A: Unable to figure out why the solution to a quadratic inequality works

If $(x-a)(x-b)\ge0$ where $a<b$ If $x-a>0,$ we need $x-b\ge0\implies x\ge b$ If $x-a\le 0,$ we need $x-b<0\implies x\le a$

Cherry_Developer

So if the graphed solution set saids that anything less than $$-\frac { 7 }{ 2 } $$ is part of the solution, why isn't -5 working?

lab bhattacharjee

@Cherry_Developer, $$-5(2\cdot-5+7)=(-5)(-3)>0$$

Cherry_Developer

-5+(7/2) gives me a number less than 0

lab bhattacharjee

@Cherry_Developer, How $$+\frac72$$ is coming

Cherry_Developer

Because x+7/2 = 0

lab bhattacharjee

11:17 AM

@Cherry_Developer, We need the product to be $\ge0$

Cherry_Developer

None of this is making sense to me.

Ok, can you explain this to me?

This is really frustrating me

what is (-4)*(-5)?

+20

but each of -4 -5<0

I understand

I get stuck at the last and mot important part of solving the quadratic inequality

would you be able to walk me through the steps?

I knew this just a few days ago and it slipped my mind

lab bhattacharjee

11:32 AM

plz.. go thru my answer

Cherry_Developer

lab bhattacharjee

pinpoint your point of confusion

Cherry_Developer

So once I arrive to X+7/2 and x+0

I solve them both

and come to x>=-7/2

and x>=0

these are my two solutions

now how does testing the values go to know what my intervals are

lab bhattacharjee

a*b >0 implies either a,b>0 or a,b both <0

Cherry_Developer

how do I test vaues

lab bhattacharjee

11:37 AM

check for <=> -7/2 and x<=>0

Cherry_Developer

so I take the value 4

and substitute x in it for both

and multiply?

so (-5+7/2)(-5+0) = +7.5

so it is >= than 0

so -5 works

correct?

then I test -1/2
(-1/2+7/2)(-1/2+0) = -1.5

-1.5 is not >= 0

so it doesn't work

is this the correct process?

I am trying this process right now and it seems to work. So I'm going to assume that I am right

last day (14 days later) »

all rooms

Transcript for

Aug '1425

Sep8

$Mathematics$ Discussion between lab bhattacharjee …

Imported from a comment discussion on math.stackexchange.com/q...

algebra-precalculus

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC

$Mathematics$