Question

If HCF of x2 + x – 20 and 2x2 – kx – 16 is x – k, then the value of k is

Answer 1

Answer:

4

Step-by-step explanation:

Given :

HCF of x² + x - 20 and 2x² - kx - 16 is x - k

Let

• f( x ) = x² + x - 20
• p( x ) = 2x² - kx - 16

So, ( x - k ) is a common factor of f( x ) and p( x )

By factor theorem

• f( k ) = 0
• p( k ) = 0

First let's make two equations out of these

⇒ f( k ) = x² + x - 20 = 0

⇒ ( k )² + k - 20 = 0

⇒ k² + k - 20 = 0  → ( 1 )

⇒ p( k ) = 2x² - kx - 16 =0

⇒ 2( k )² - k( k ) - 16 = 0

⇒ 2k² - k² - 16 = 0

⇒ k² - 16 = 0 →  ( 2 )

Subtracting ( 1 ) from ( 2 ) we get,

⇒ k² - 16 - ( k² + k - 20 ) = 0

⇒ - 16 - k + 20 = 0

⇒ 4 - k = 0

⇒ 4 = k

⇒ k = 4

Therefore the value of k is 4.