Question

Find the value of m in order that x4 – 2x3 + 3x2 – mx + 5 is exactly divisible by x – 2.

Answer 1

Answer:

m=24.5

if I am not wrong..........

Answer 2

Answer :

The required value of m is '8.5'

Step-by-step explanation :

Given :

x⁴ – 2x³ + 3x² – mx + 5 is exactly divisible by x – 2

To find :

the value of m

Solution :

Let p(x) = x⁴ – 2x³ + 3x² – mx + 5

If the given polynomial x⁴ – 2x³ + 3x² – mx + 5 is exactly divisible by x – 2, then the remainder is zero.

 

➛ x – 2 = 0

➛ x = +2

By remainder theorem,

If p(x) is divisible by (x - a) , then p(a) = 0

So, when we substitute x = 2, the result is zero.

  p(2) = 0

➙ (2)⁴ – 2(2)³ + 3(2)² – m(2) + 5 = 0

➙ 16 - 2(8) + 3(4) - 2m + 5 = 0

➙ 16 - 16 + 12 - 2m + 5 = 0

➙ 12 - 2m + 5 = 0

➙  17 - 2m = 0

➙  2m = 17

➙  m = 17/2

➙  m = 8.5

Therefore, the value of m is 8.5