If the sum of the roots of x^3+x^2-14x-24=0 is subtracted from the product of the roots of the same equation?

Question

what is the result?

Answer 1

Please give your math homework an honest try. This has to be at least the third question you've asked.


Method 1: Factor the polynomial. Synthetic division is a quick and easy to learn factoring tool. You can learn it here: http://www.purplemath.com/modules/synthdiv.htm

Method 2: Graph it on a graphing calculator and find the zeros.

Either way works quite well, although the calculator isn't always the most precise.

Answer 2

The product of the roots of x^3+x^2-14x-24=0 is given by the negative of the constant term -(-24) = 24. The sum of the roots is given by the negative of the coefficient of x^2, which is -(1) = -1. Thus, we want 24 - (-1) = 25.

Answer 3

Any cubic equation with roots r1, r2 and r3 will be:

(x - r1)(x - r2)( x - r3) = 0.

This will be, after full expansion:

x^3 - (r1 + r2 + r3)x^2 + (r1r2+r2r3+r3r1) - r1r2r3 = 0.

In our case, it is given:

x^3 + x^2 -14x - 24 = 0. So just by comparison:

Sum of the roots = r1 + r2 + r3 = - 1 &

Product of the roots = r1r2r3 = 24.

So that:

Product of the roots - (sum of the roots) = 24 - ( - 1) = 25.

Answer 4

A cubic is (x - r1)(x - r2)(x - r3) for the 3 roots r1, r2, r3. If you multiply this out you get x^3 - (r1 + r2 + r3)x^2 + (something)x - r1r2r3

So the sum you want is just -1, and the product is 24, so sum - product is -25