Question from RD Sharma find the value of k if x-3 is a factor of k^2x^3 - kx^2 + 3kx - k

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Polynomial p(x) has a factor x-3 if and only if p(3)=0.

Here p(3)=27*k^2 -9k + 9k - 9k - k = 27*k^2 - k = 0.

So k=0 or k=1/(3√3) or -1/(3√3).

Please ask if anything is unclear.

balajia | Student

 (x - 3) is a factor of `k^2*x^3 - k*x^2 + 3*k*x - k`

so f(3) = 0 
==>`k^2*(3)^3 - k*(3)^2 + 3*k*(3) - k =0`
 ==>` 27*k^2 - 9*k + 9k - k = 0`

=> `27*k^2 - k = 0`
==> `k(27k - 1) = 0`

Hence k = 0 or k = `1/27`