Apolynomial 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 )