Question

How do you solve `2x ^ { 2} - x - 15= 0`?

Answer 1

`x= -5/2 and x= +3`

Explanation:

You must find factors of the (`2x^2`) term and the (-15) term which give a (-x) term. In this situation it will be:

`" "2x^2 -x -15`

`" "2xcolor(white)(xxxxxx)5`
`" "1xcolor(white)(xxxxxx)3`

Cross multiply and subtract so:

`" "2xcolor(white)(xxxxx)+5" "rarr 1x xx +5 = +5x`
`" "1xcolor(white)(xxxxx)-3" "rarr 2x xx -3= -6x`

So you have: `" " 2x xx-3 = -6x and x xx5 = +5x`

The total is what you want:`-6x+5x = -x`

So your answer is: `(2x+5)(x-3) =0`

Setting each factor = 0 gives:

The roots are `-5/2 and +3`