Thread: urgent.i have exam tmr.roots & remainder

the cubic polynomial f(x) is such that the coefficient of x^3 is 1 and the roots of f(x)=0 are 1, k , k^2 . it is given that f(x) has a remainder of 7 when divided by x-2.

show that k^3 - 2k^2 - 2k - 3 =0.

thanks teach me how to solve. thank you very much

Originally Posted by helloying

the cubic polynomial f(x) is such that the coefficient of x^3 is 1 and the roots of f(x)=0 are 1, k , k^2 . it is given that f(x) has a remainder of 7 when divided by x-2.

show that k^3 - 2k^2 - 2k - 3 =0.

thanks teach me how to solve. thank you very much

.. a=1 so



.. expand this part



Here you can compare

--- 1

--- 2

----------------------------------------

Now make use of the factor and remainder theorem

You know one of the factors is (x-1) so

f(1)=0

--- 3

Then it will give a remainder of 7 when divided by (x-2)

f(2)=7

--- 4

4-3

Now look back . From 2 above , --6
(Replace the c with -3b)

Multiply 1 by 3 ... -- 5

6-5 i will leave this for you .

Hi helloying
The factors are x = 1, x = k, and x = k^2, so :

(x-1)(x-k)(x-k^2) = 0

f(x) = (x-1)(x-k)(x-k^2)

Subs. x = 2