Thread: Algebra Help

Cubic Equations

Q -
(i) Find the three linear factors of x³ + 5x² - 2x - 24.
(ii) Hence, or otherwise, solve the equation x³ + 5x² - 2x - 24 = 0

Please supply a formula aswell so I can solve these in the future! Thankyou




PLEASE HELP! VERY VERY URGENT

Originally Posted by emrldz

Q -
(i) Find the three linear factors of x³ + 5x² - 2x - 24.
(ii) Hence, or otherwise, solve the equation x³ + 5x² - 2x - 24 = 0

Please supply a formula aswell so I can solve these in the future! Thankyou




PLEASE HELP! VERY VERY URGENT

Hello,

the good news first: There exists a formula to solve cubic equation: Cardano's formula. It is very complicated and therefore it is very easy to make a lot of silly mistakes.

I can only sho you how I would do your problem:
1. The question indicates that there are rational solutions.
2. Try to find one solution. It must be a factor of 24. I've found x = 2 is a solution because:

3. Now use synthetic division:

Code:

      |  1    5     -2    -24          <---all coefficients
      |  0    2     14     24
------|-------------------------
x = 2 |  1   7      12      0         <---next guess: x = -3
      |  0   -3     -12
------|-------------------------
x = -3| 1    4      0

From the last row you know

Therefore:

A product equals zero if one of the factors equal zero: