given that f(x)= and when f(x) is divided by (x-k) the remainder is k. find the possible values for k.
i have
am stuck here. i know that (k-1) is a factor but i get a reaminder when i divide the equation by it,
may i get some help with this?
Perhaps you tried to divide by ? - That doesn't work out as expected to be sure. But what about dividing by ?
In this case I get k-1)=2k^2+2k-1" alt="(2k^3-3k+1)k-1)=2k^2+2k-1" />.
Moral: you have to move everything to one side of the equation before trying the division by .
The other two values of k that are solutions to the original equation are irrational, so you can't find them by "educated guessing": you have to solve the quadratic equation by whatever other means available (such as applying a memorized formula for that, or simply "completing the square").
By the rational root theorem, the only possible rational roots are 1, -1, 1/2, and -1/2. Putting those into the equation, , , , and .
Since 1 is a root, has k- 1 as a factor: . You can use the quadratic formula to find the other two roots.
Then youare dividing wrong!am stuck here. i know that (k-1) is a factor but i get a reaminder when i divide the equation by it,
may i get some help with this?