Question

Let f(x) be a polynomial such that f ( - 1/2) = 0, then a factor of f(x) is
A. 2x -1
B. 2x+1
C. x-1
D. x +1

Answer 1

Given:  Let f(x) be a polynomial such that f ( - 1/2) = 0

 

To find : factor of f(x)  

 

Solution :  

Let f(x) be a polynomial and f (-½ ) = 0, then  

x + ½  = 0

[p(a) = 0 , then (x - a) is a factor of p(x)]

0 = (2x + 1)/2  

= 2x + 1  

Hence, 2x + 1 is a factor of f (x)

Among the given options option (B) 2x + 1 is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

Similar questions :

If x+1 is a factor if the polynomial 2x²+kx, then k =

A. -2

B. -3

C. 4

D. 2

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If x+1 is a factor if the polynomial 2x²+kx, then k =

A. -2

B. -3

C. 4

D. 2

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Answer 2

Answer: Opt. B) 2x + 1

Step by step explanation:

Given that: f(x) is a polynomial such that f(-1/2) = 0

To find: The factor of f(x)

Solution:

If f(-1/2) is a solution of he polynomial f(x), then:

x = -1/2 __(1)

This means that:

When the value of x is equal to -1/2, then the polynomial results in 0

When we solve the above equation (1), we get:

x = -1/2

x + 1/2 = 0

Take the LCM:

( 2x + 1 )/2 = 0

Take 1/2 on the RHS:

2x + 1 = 0

Thus, the factor is 2x + 1

Option (B) is right.