Mammoth Memory

Using the quadratic formula solver Example 3

Solve           `2x^2-6x+3=0`

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

Quick sketch

Therefore   `a=2` , `b=-6`  &  `c=3`

`x=(-(-6)+-sqrt((-6)^2-4times2times3))/(2times2)`

`x=(6+-sqrt(36-24))/4`

`x=(6+-sqrt12)/4`

`x=(6+sqrt12)/4`   or  `x=(6-sqrt12)/4`

Using a calculator we get

`x=(6+5.165)/4`   or  `x=(6-5.165)/4`

`x=2.366`   or  `x=0.634`

 

Now check the answer

`2x^2-6x+3=0`

 

If `x=2.366`            `2times2.366^2-6times2.366+3=0`

`11.19-14.19+3=0`  Which is correct

If `x=0.634`            `2times0.634^2-6times0.634+3=0`

`0.804-3.804+3=0`  Which is correct

Answer:

The roots of `2x^2-6x+3=0`   are  `x=2.366`   or  `x=0.634`