Question

How to factorize this? `2x^2-6x+3`

Answer 1

You can not derive whole number factors for this question
`x=3/2+-sqrt(3)/2` Exact values

`x~~2.366 and 0.634` Approximate values

Explanation:

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

Compare to `y=ax^2+bx+c` where `a=2;b=-6;c=3`

Worth committing this on to memory `x=(-b+-sqrt(b^2+4ac))/(2a)`

`x=(+6+-sqrt(6^2-4(2)(3)))/(2(2))`

`x=3/2+-sqrt(12)/4`

`x=3/2+-sqrt(3xx4)/4`

`x=3/2+-(2sqrt(3))/4`

`x=3/2+-sqrt(3)/2`

`x~~2.366 and 0.634` to 3 decimal places

Answer 2

`(2(x-3/2-sqrt3/2)(x-3/2+sqrt3/2)`

Explanation:

`"take out a common factor of 2"`

`rArr2x^2-6x+3=2(x^2-3x+3/2)`

`"find the roots of the quadratic hence the factors"`

`"using the "color(blue)"quadratic formula"`

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

`a=1,b=-3" and "c=3/2`

`x=(3+-sqrt(9-6))/2=3/2+sqrt3/2`

`rArrx^2-3x+-3/2`

`=(x-(3/2+sqrt3/2))(x-(3/2-sqrt3/2))`

`=(x-3/2-sqrt3/2)(x-3/2+sqrt3/2)`

`rArr2x^2-6x+3`

`=2(x-3/2-sqrt3/2)(x-3/2+sqrt3/2)`