Question

Find the value of k if extho is factor

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Answer 1

Step-by-step explanation:

Consider the given polynomial.

Consider the given polynomial.x

Consider the given polynomial.x 4

Consider the given polynomial.x 4 −k

Consider the given polynomial.x 4 −k 2

Consider the given polynomial.x 4 −k 2 x

Consider the given polynomial.x 4 −k 2 x 2

Consider the given polynomial.x 4 −k 2 x 2 +3x−6k

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−k

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k)

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k)

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4 −k

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4 −k 4

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4 −k 4 −3k−6k=0

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4 −k 4 −3k−6k=0−9k=0

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4 −k 4 −3k−6k=0−9k=0k=0

Consider the given polynomial.x 4 −k 2 x 2 +3x−6kSince, x+k is the factor of given polynomial So, put x=−kTherefore,(−k) 4 −k 2 (−k) 2 +3(−k)−6k=0k 4 −k 4 −3k−6k=0−9k=0k=0Hence, the value of k is 0.

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