Question

Identify all factors of the expression 12x^2-14x-6

Answer 1

Let's solve this by using the quadratic formula:

$\frac{-b+-\sqrt{b^2-4ac} }{2a}$

Note that we only use the coefficients so a=12, b=-14, and c=-6.

Plug values in the quadratic equation:

$\frac{ - ( - 14)± \sqrt{ {( - 14)}^{2} - 4(12)( - 6) } }{2(12)}$

And so by evaluating those values we obtain:

$\frac{14+-\sqrt{484} }{24}=\frac{14+-22}{24}$

Now we have two answers which are our factors one where we add another where we subtract and so:

First factor:

$\frac{14+22}{24}=\frac{36}{24}=\frac{3}{2}$

Second Factor:

$\frac{14-22}{24}=\frac{-8}{24}=-\frac{1}{3}$

And so your factors are

$\frac{3}{2},-\frac{1}{3}$

meaning that those are your roots/x-intercepts.