$\large x^3 - 12 x^2 + 47 x -60 =0$

If $a$ , $b$ , $c$ are roots of the above polynomial. Find the value of $|\left(a-b \right) \left(b-c \right) \left(c-a \right)|$ .

The answer is 2.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

Method I: Without finding the roots, we know that the product we seek is the square root of the discriminant, by definition. The formula for the discriminant gives $\sqrt{4}=\boxed{2}$

Method 2: The roots are easily seen to be 3,4, and 5