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What is the value of k if x-3is a factor of the polynomial k²x³-kx²+3kx-k?

Posted by Arpan Nema 8 years, 6 months ago

CBSE > Class 09 > Mathematics

1 answers

Payal Singh 8 years, 6 months ago

p(x) = k²x³-kx²+3kx-k

As x-3 is factor of p(x) so x= 3 is zero of this polynomial.

Using remainder theorem

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

=> k = 0 or 27k-1=0

=> k = 0 or {tex}1\over 27{/tex}

1Thank You

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