Question

One root of mc020-1.jpg is x = 2. What are all the roots of the function? Use the Remainder Theorem.

Answer 1

 The given polynomial is f(x) = x3- 9x2 + 26 x -24. if the one root is equal to 2, then we can determine the other roots by synthetic division: 

2 |  1   -9    26    -24
           2    -14     24
       1  -7     12     0

x2 -7x + 12 = (x-3)(x-4)

as a correction, we used root of -2 to determine the other roots. the other roots then are 3 and 4.

Answer 2

The roots of the equation will be 2, 3 and 4

Remainder theorem of polynomial

Given the  given polynomial function g(x) = x³- 9x² + 26 x -24. if the one root is equal to 2, then we can determine the other roots by synthetic division:

q(x) = g(x)/d(x)

q(x) = x³- 9x² + 26 x -24/x - 2

q(x) = x² -7x + 12

Factorize the result to have:

x² -7x + 12 = 0

x² -4x - 3x + 12 = 0

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

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

x = 3 and 4

Hence the roots of the equation will be 2, 3 and 4

Learn more on remainder theorem here: https://brainly.com/question/13328536