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Mkey [24]
3 years ago
5

Identify all of the roots of the function.

Mathematics
2 answers:
Yuki888 [10]3 years ago
6 0

The <u>integer roots</u> of the <u>polynomial function</u> f(x)=x^3-5x^2-2x+24 can be only among the<u> divisors</u> of <u>free term</u>.

The divisors of free term are:

\pm 1, \pm 2, \pm 3,  \pm 4, \pm 6, \pm 8, \pm 12, \pm 24.

Check them:

1. f(1)=1^3-5\cdot 1^2-2\cdot 1+24=18\neq 0, 1 is not a root.

2. f(-1)=(-1)^3-5\cdot (-1)^2-2\cdot (-1)+24=20\neq 0, -1 is not a root.

3. f(2)=2^3-5\cdot 2^2-2\cdot 2+24=8\neq 0, 2 is not a root.

4. f(-2)=(-2)^3-5\cdot (-2)^2-2\cdot (-2)+24=0, -2 is a root.

5. f(3)=3^3-5\cdot 3^2-2\cdot 3+24=0, 3 is  a root.

6.  f(-3)=(-3)^3-5\cdot (-3)^2-2\cdot (-3)+24=-42\neq 0, -3 is not a root.

7. f(4)=4^3-5\cdot 4^2-2\cdot 4+24=0, 4 is  a root.

The cubic function has at most 3 roots, then

Answer: roots of the function are -2, 3 and 4.

Ksju [112]3 years ago
5 0
F(x) = x3 - 5x2 - 2x + 24

roots -2, 3 and 4
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