Question

Find the value of k,if x-1 is a factor of p(x) which is 2xsquare+kx+root2

Answer 1

Question:

Find the value of K for which (x-1) is a factor of p ( x ) which is 2x² + kx + √2.

Answer:

The value of k is - √2 ( 1 + √2 ).

Step-by-step-explanation:

The given polynomial is p ( x ) = 2x² + kx + √2.

We have given that,

( x - 1 ) is a factor of the given polynomial.

By factor theorem,

If x = 1, p ( x ) = 0

∴ 2 * ( 1 )² + k * 1 + √2 = 0

⇒ 2 * 1 + k + √2 = 0

⇒ 2 + k + √2 = 0

⇒ k = - 2 - √2

⇒ k = - √2 ( √2 + 1 )

⇒ k = - √2 ( 1 + √2 )

∴ The value of k is - √2 ( 1 + √2 ).