Question

Factor the quadratic expression WITH FORMULA 6x^2 - x - 12=0

Answer 1

Recall that the quadratic formula states that the solutions to the equation:

`ax^2+bx+c=0`

are:

`x=(-b\pm√(b^2-4ac))/(2a).`

Therefore the solutions to the given equation are:

`x=(-(-1)\pm√((-1)^2-4(6)(-12)))/(2(6)).`

Simplifying the above result we get:

`x=(1\pm√(1+288))/(12)=(1\pm√(289))/(12)=(1\pm14)/(12).`

Then the solutions to the given equation are:

`x=(1-14)/(12)=-(13)/(12)\text{ and x=}(1+14)/(12)=(15)/(12)=(5)/(4).`

Answer:

`x=-(13)/(12)\text{ and }x=(5)/(4).`