Question

What are the solution(s) of: `3x^2 - 8x + 5 = 0`?

Answer 1

`x=5/3, 1`

Explanation:

`3x^2-8x+5=0`

`(3x-5)(x-1)=0` factorise

`3x-5=0 or x-1=0` solve

`therefore x=5/3, 1`

Answer 2

`x=1" or "x=5/3`

Explanation:

`"using the a-c method to factorise"`

`"the factors of the product "3xx5=15`
`"which sum to - 8 are - 3 and - 5"`

`"split the middle term using these factors"`

`3x^2-3x-5x+5=0larrcolor(blue)"factor by grouping"`

`color(red)(3x)(x-1)color(red)(-5)(x-1)=0`

`"take out the common factor "(x-1)`

`rArr(x-1)(color(red)(3x-5))=0`

`"equate each factor to zero and solve for x"`

`x-1=0rArrx=1`

`3x-5=0rArrx=5/3`