Find the
value of K, if x-1 is a factor of
p(x) in each of the following
cases
ing
i)p(x) = x^2+x+k
ii) p(x).=2x² + kx + √2
iii) p (x) = Kx² - √2x + 1
IV)p(x)=kx^2-3x+k
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Answer :
i ) p( x ) = x² + x + k
x - 1 is the factor of p( x )
By factor theorem
=> p( 1 ) = 0
=> 1² + 1 + k = 0
=> 1 + 1 + k = 0
=> 2 + k = 0
=> k = - 2
ii ) p( x ) = 2x² + kx + √2
x - 1 is the factor of p( x )
By factor theorem
=> p( 1 ) = 0
=> 2( 1 )² + k( 1 ) + √2 = 0
=> 2 + k + √2 = 0
=> k = - 2 - √2
iii) p( x ) kx² - √2 x + 1
x - 1 is the factor of p( x)
By factor theorem
=> p( 1 ) = 0
=> k( 1 )² - √2 ( 1 ) + 1 = 0
=> k - √2 + 1 = 0
=> k = √2 - 1
iv) p( x ) = kx² - 3x + k
x - 1 is the factor of p( x)
By factor theorem
=> p( 1 ) = 0
=> k( 1 )² - 3( 1 ) + k = 0
=> k - 3 + k = 0
=> 2k = 3
=> k = 3/2
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