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 Reply
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Step-by-step explanation:
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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