Question

Find the value of k for which (x - 2) is factor of x ^ 2 + (4 - k) * x + 2​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The value of k is 7.

Step-by-step-explanation:

The given polynomial is x² + ( 4 - k ) x + 2.

Let the polynomial be P ( x ).

We have given that,

( x - 2 ) is a factor of the given polynomial.

By factor theorem,

If x = 2, P ( x ) = 0

∴ ( 2 )² + ( 4 - k ) * 2 + 2 = 0

⇒ 4 + 8 - 2k + 2 = 0

⇒ 12 - 2k + 2 = 0

⇒ - 2k + 12 + 2 = 0

⇒ - 2k + 14 = 0

⇒ - 2k = - 14

⇒ 2k = 14

⇒ k = 14 ÷ 2

⇒ k = 7

∴ The value of k is 7.