# How do you solve #3x^2+5x-2=0#?

##### 3 Answers

#### Explanation:

Factorise to get

hence

giving

#### Explanation:

Find factors of 3 and 2 which subtract to make 5.

We should realise that (3x2) - 1 = 5.

Find the cross products and subtract to get 5.

#3" "1 " "rArr 1xx1 =1 #

#1" "2" "rArr 3xx2 = 6 " "(6-1 = 5)#

Add in the signs.

#3" "-1 " "rArr 1xx-1 =-1 #

#1" "+2" "rArr 3xx+2 = +6 " "(+6-1 = +5)#

One of the factors must be 0.

If

If

There is only one way to deal with factorization. That is lots of practice.

#### Explanation:

Given:

'............................................................................................................

Both 3 and 2 are prime numbers so they can only be the products of:

for 2

for 3

So without taking any notice of the signs (sorted out afterwards) we have something like:

I have kept both

Notice that

giving

So the factor form is very likely:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check:

Multiplying out the brackets

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So we have:

Note that anything

This means that the solution is such that