x^3 - 10x^2 + 13x + 24= 0?

Question

What is x?

Answer 1

f(-1) = - 1 - 10 - 13 + 24 = 0
Thus x - (- 1) = x + 1 is a factor.
To find other factors use synthetic division:-
_|1 __-10__13__24
-1|____-1__11_-24
_|1__- 11__24__0

(x + 1)(x² - 11x + 24) = 0
(x + 1)(x - 8)(x - 3) = 0
x = - 1 , x = 8 , x = 3

Answer 2

3 is a root of the equation, because when you put x=3 the result is 0.

So we divide it by (x-3):

(x^3 - 10x^2 + 13x + 24) : (x-3)

=

(x-3)*(x^2-7x-8)

which can then be broken down further into:

(x-3)*(x+1)*(x-8)

So x is either 3, -1 or 8.

I hope this helped.
Please don't forget to put my answer as best answer, thank you!

Answer 3

x^3 --10x^2 + 13x + 24 = 0
=> x^3 -- 3x^2 -- 7x^2 + 21x -- 8x + 24 = 0
=> x^2(x -- 3) -- 7x(x -- 3) -- 8(x -- 3) = 0
=> (x -- 3)(x^2 -- 7x -- 8) = 0 giving x = 3 answer (1).
=> x^2 -- 7x -- 8 = 0
=> (x -- 8)(x + 1) = 0 giving x = 8, --1. answers(2,3).
whencw x = 3, 8, --1.

Answer 4

x³ - 10x² + 13x + 24 = 0

x³ - 3x² - 7x² + 21x - 8x + 24 = 0

(x²)(x - 3) - (7x)(x - 3) - (8)(x - 3) = 0

(x - 3)( x² - 7x - 8) = 0

(x - 3) (x - 8) (x +1) = 0

So,

x = 3, 8, -1

Answer 5

Answers are -1 and 3.

Answer 6

Use synthetic division followed by the quadratic equation (if necessary).