Question

Find the value of k, if x=3 is a factor of
k²x³-kx² + 3kx-k​

Answer 1

Let f(x) be the given polynomial.

f(x)=k²x³-kx²+3kx-k

Given that x=3

If (x - @) is a factor of a polynomial,then @ is zero of a polynomial

So,

f(x)=f(3)

Substituting the required value,

f(3)=k²x³-kx²+3kx-k

→0 = k²(3)³-k(3)²+3k(3)-k

→0=27k²-9k+9k-k

→27k²-k=0

→k(27k-1)=0

→k=0 or 27k=1

→k=1/27 or 0

Answer 2

Given p(x) = k²x³ - kx² + 3kx - k

given one zero of p(x) = 3

then,

p(3) = 0

k²(3)³ - k(3)² + 3k(3) - k = 0

27k² - 9k + 9k - k = 0

27k² - k = 0

k(27k - 1) = 0

27k - 1 = 0

27k = 1

k = 1/27

so,

k = 1/27