Question

if x-2 is a factor of a polynomial f(x)=x⁵-3x⁴-ax³ +3ax² +2ax+4 ,then find the valie of a..​

Answer 1

Answer:

3/2

Step-by-step explanation:

Given f(x) = x^5 - 3x^4 - ax^3 + 3ax^2 + 2ax + 4.

Given g(x) = x - 2.

By the remainder theorem, 

x - 2 = 0

x = 2.

Plug x = 2 in f(x), we get

f(2) = (2)^5 - 3(2)^4 - a(2)^3 + 3a(2)^2 + 2a(2) + 4 = 0

      = 32 - 48 - 8a + 12a + 4a + 4 = 0

      = -16 + 4 + 8a = 0

      = -12 + 8a = 0

     8a = 12

      a = 12/8

      a = 3/2.

Therefore the value of a = 3/2.

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Answer 2

ANSWER:

• Value of a is 3/2

GIVEN:

• (x-2) is a factor of a polynomial f(x)=x⁵-3x⁴-ax³ +3ax² +2ax+4.

TO FIND:

• Value of 'x'

SOLUTION:

f(x)=x⁵-3x⁴-ax³ +3ax² +2ax+4

g(x) = x-2

Using remainder theorem

Let (x-2) = 0

=> x = 2

(x-2) is a factor of f(x) then remainder should be equal to 0.

Putting x = 2 in f(x) .we get remainder = 0

f(2) = (2)⁵-3(2)⁴-a(2)³+3a(2)²+2a(2)+4

=> 32-48 -8a+12a+4a+4 = 0

=> 32+4-48+8a = 0

=> -12 +8a = 0

=> 8a = 12

=> a = 12/8

=> a = 3/2

Value of a is 3/2

NOTE:

• This type of question can be solved by using remainder theorem.