Question

if x+1 and x-1 are the factor of mx^3+x^2-2x+n find the value of mand n​

Answer 1

Given:-

• x+1 and x-1 are the factor of mx^3+x^2-2x+n.

To find:-

• The value of m and n.

Solution:-

→As x+1 and x-1 are factor of the polynomial,

     x + 1 = 0      or    x - 1 = 0

→so,  x  = -1 or 1.

Let x=1  :

⇒ mx³+x²-2x+n=0

⇒ m(1)³+(1)²-2(1)+n=0

⇒ m+1-2+n=0

⇒ m+n-1=0   ⇒  m+n=1----(1)

If  x=-1  :

⇒  m(-1)³+(-1)²-2(-1)+n=0

⇒ -m+1+2+n=0 ⇒  m-n=3---(2)

→ adding  (1)and(2)  :

⇒ 2m=4

⇒m=2

put m=2 in (1)

⇒ 2+n=1

⇒ n=-1

∴ (m,n)=(2,-1)

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