A polynomial function has roots - 5 and 1. Which of the following could represent this function?

(x) = (x + 5) (x + 1)

f (x) = (x - 5) (x - 1)

f (x) = (x - 5) (x + 1)

f (x) = (x + 5) (x - 1)

Option D is correct. i. e., f (x) = (x + 5) (x - 1)

Step-by-step explanation:

Given: Roots of Polynomial are - 5 and 1

To find: Polynomial function

We substitute given value of roots in each polynomial and check

if for both value polynomial given 0 then that our required polynomial

A). f (x) = (x + 5) (x + 1)

for x = - 5

f (-5) = (-5 + 5) (-5 + 1)

= 0 * (-4) = 0

for x = 1

f (1) = (1 + 5) (1 + 1)

= 6 * 2 = 12 ≠ 0

Thus, It is not required polynomial

B). f (x) = (x - 5) (x - 1)

for x = - 5

f (-5) = (-5 - 5) (-5 - 1)

= - 10 * (-6) = 60 ≠ 0

for x = 1

f (1) = (1 - 5) (1 - 1)

= - 4 * 0 = 0

Thus, It is not required polynomial

C). f (x) = (x - 5) (x + 1)

for x = - 5

f (-5) = (-5 - 5) (-5 + 1)

= - 10 * (-4) = 40 ≠ 0

for x = 1

f (1) = (1 - 5) (1 + 1)

= - 4 * 2 = - 8 ≠ 0

Thus, It is not required polynomial

D). f (x) = (x + 5) (x - 1)

for x = - 5

f (-5) = (-5 + 5) (-5 - 1)

= 0 * (-6) = 0

for x = 1

f (1) = (1 + 5) (1 - 1)

= 6 * 0 = 0

Thus, It is required polynomial

Therefore, Option D is correct. i. e., f (x) = (x + 5) (x - 1)

Te that's is a function