Answer:
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 )
