Solve the equation: (4x − 6)(2x − 5) = 0

Question

parthkohli · Answer

Do you want me to teach this to you?

mathslover · Answer

k parth u carry on

mathslover · Answer

@jiteshmeghwal9 please dont answer

jiteshmeghwal9 · Answer

i mn't giving answer

mathslover · Answer

ok .. parth u carry on with ur teaching

jiteshmeghwal9 · Answer

i wanna let him understnd

parthkohli · Answer

Okay, @herbdog 
You need to be familiar with 'zero-product-rule' okay?
The name is intimidating, but it's understandable.

parthkohli · Answer

Have you heard that if you multiply 0 to a number, then you get 0?

anonymous · Answer

yes

jiteshmeghwal9 · Answer

now let me teach also

parthkohli · Answer

So, maybe 2x - 5 is 0.. that may be the reason why we have 0.

parthkohli · Answer

Or maybe 4x - 6 is 0.

parthkohli · Answer

Get it till now? @herb

anonymous · Answer

yes

parthkohli · Answer

So we can have two $x$'s here, because we have two numbers that makes this zero.

parthkohli · Answer

Can we now say that either $4x - 6 = 0$ or $2x - 5 = 0$?

anonymous · Answer

yeah

parthkohli · Answer

So as I taught you - can you solve these two equations?$$4x - 6  = 0\2x - 5=0 $$These are two different equations, all right?

anonymous · Answer

okay, but cant we subtract the two equations or no?

jiteshmeghwal9 · Answer

If given a polynomial, we sometimes want to know for which value of 'x' it is zero . For example: we solved linear equations of the type 2x+3=0 . we find that x=-3/2 is a solution to this equation. another way to say the same thing is that -3/2 is a zero of the polynomial. & remember it depends on the equation that how many zeros are founded.

parthkohli · Answer

No, herb. They are not the same equations. 
Two different equations that you have to solve differently.

anonymous · Answer

oh, so if they different how do we solve it

parthkohli · Answer

First solve this equation for me:$$4x  - 6 = 0 $$

anonymous · Answer

isnt it -2x=0

parthkohli · Answer

Nope. Add 6 to both sides.

anonymous · Answer

ooh becomes 4x=6

parthkohli · Answer

Yeah, now divide both sides by 4.

anonymous · Answer

becomes 1.5

parthkohli · Answer

Right - there's one solution. You have to get another solution by solving$$2x - 5 = 0 $$

anonymous · Answer

so i add 5 to both sides becomes 2x=5 right?

parthkohli · Answer

Yes! You getting it! Now divide both by 2.

anonymous · Answer

and i get 2.5

parthkohli · Answer

Woo! There you go!
The two solutions are 1.5 and 2.5!

anonymous · Answer

so x = 1.5 & 2.5

parthkohli · Answer

That's it :)

anonymous · Answer

thanks that helped alot

parthkohli · Answer

I bet it did. You're welcome :)