Question

X³ - 3x² -10x + 24 = 0 please give step by step answer

Answer 1

Answer:

Hope this helps you....

Answer 2

We don't know one of the factors, and it is third power.

Solution: We have rational roots theorem.

It is proven that possible solutions are between ±(factors of 24). So possible roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Let's see if x=2 is a solution.

If we put x=2, the polynomial x³ - 3x² - 10x + 24 = 0 is true. ∴x=2 is a solution.

Now one root is found to be 2. Next, we should use factor theorem.

Solution: x-2=0 so it is divisible by x-2.

Divide x³ - 3x² - 10x + 24 by x - 2 and the quotient is x² - x - 12.

As x² - x - 12 = (x + 3)(x - 4) two other factors are x+3 and x-4.

Therefore, (x-2)(x+3)(x-4)=0. Hence the solutions are x=2 or x=-3 or x=4.