Using the quadratic formula solver Example 1

Solve `3x^2-7x+2=0` 

Use the quadratic formula solver

`x=(-b+-sqrt(b^2-4ac))/(2a)`

Quick sketch

Therefore  `a=3` , `b=-7` , & `c=2`

`x=(-(-7)+-sqrt((-7)^2-4times3times2))/(2times3)`

`x=(7+-sqrt(49-24))/6=(7+-sqrt25)/6=(7+-5)/6`

`x=12/6`  and   `x=2/6`

`x=2`  and   `x=1/3`

 

So  `x=2`  and `1/3`  is the answer.

 

Now check this is correct

`3x^2-7x+2=0`

 

If `x=2`              `3times2^2-7times2+2=0`

`12-14+2=0`  Which is correct

If `x=1/3`             `3times(1/3)^2-7times(1/3)+2=0`

`3/9-7/3+2=0`

`1/3-2\1/3+2=0`  Which is correct

 

(If they don't add up to zero you can be assured that it is wrong).

Answer:

The roots of `3x^2-7x+2=0`   are  `x=2`   or  `1/3`