Question

If (x-1) is a factor of x4 – 5x3+ax2 +5x-k then a-k =
(A) -1
(B) 1
(C) 0

Answer 1

Answer:

a - k = -1

Step-by-step explanation:

If x-1 is the factor then-

x - 1 = 0

x = 1

p(x) = x⁴ - 5x³ + ax² + 5x - k

If x=1 then p(x) must be zero

p(1) = (1)⁴ - 5(1)³ + a(1)² + 5(1) - k = 0

p(1) = 1 - 5 + a + 5 - k = 0

p(1) = 1 + a - k = 0

      = a - k = -1

Option (a) is correct

Answer 2

A) the value of a – k is -1.

Step-by-step explanation:

Given: Factor of x⁴ – 5x³ + ax² +5x – k is (x – 1)

To Find: a – k

Solution:

• Finding the value of a – k

Since x – 1 is a factor, therefore, x – 1 = 0 ⇒ x = 1

Now, substituting x = 1 in the polynomial equation x⁴ – 5x³ + ax² +5x – k, we get,

⇒ (1)⁴ – 5(1)³ + a(1)² + 5(1) – k = 0

⇒ 1 – 5 + a + 5 – k = 0

⇒ 1 + a – k = 0

⇒ a – k = -1

Hence, the value of a – k is -1.