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3 years ago

One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.

Mathematics

2 answers:

True [87]3 years ago

6 0

Answer:

The roots of the of the function are 2,3 and 4.

Step-by-step explanation:

The given function is

f(x) = x³ - 9x² + 26x - 24

It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).

According to the remainder theorem if a function is divided by (x-c), then the remainder is equal to f(c). If f(c) is equal to 0, therefore c is the root of the function.

Use synthetic method to divide f(x) by (x-2).

f(x) = (x - 2) (x² - 7x + 12)

f(x)= (x - 2) (x² - 4x - 3x + 12)

f(x)= (x - 2) (x(x - 4) - 3(x - 4))

f(x)= (x - 2) (x - 4) (x - 3)

To find the roots equation the function equate the function equal to 0.

0 = (x - 2) (x - 4) (x - 3)

Equate each factor equal to 0.

x = 2,3,4

Therefore the roots of the function are 2,3 and 4.

(btw this is someone else's answer i found since i got a little confused myself heh)

Phantasy [73]3 years ago

4 0

Answer:

The roots of the of the function are 2,3 and 4.

Step-by-step explanation:

\The roots of the of the function are 2,3 and 4.

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Step-by-step explanation:

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Sophie [7]

Step-by-step explanation:

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