250 Followers Problem - 2

Algebra Level 3

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

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.

2 solutions

Otto Bretscher
Oct 31, 2015

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

Could you please tell the formula of discriminant..

Rakshit Joshi - 5 years, 7 months ago

b2-4ac is the formula but this is for squre equation...

Adnan Malik - 5 years, 7 months ago

Tom Engelsman
Feb 12, 2019

The above cubic factors into:

$x^2 - 12x^2 + 47x - 60 = (x-3)(x-4)(x-5)$

with roots $x = 3,4,5$ . Thus, $|(3-4)(4-5)(5-3)| = \boxed{2}.$

250 Followers Problem - 2

The answer is 2.

2 solutions

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