Question

If x+1 and x-1 are factors of 2x^3+mx^2+nx-3 determine the values of m and n

Answer 1

Answer:

m = 3 & n = - 2

Step-by-step explanation:

If x + 1 and x - 1 are factors of 2x^3+mx^2+nx-3, value of this polynomial must be 0, for x = - 1 or x = 1.

For x = - 1:

= > 2(-1)³ + m(-1)² + n(-1) - 3 = 0

= > 2(-1) + m(1) + n(-1) - 3 = 0

= > - 2 + m - n - 3 = 0

= > m - n - 5 = 0

= > m - n = 5 ... (1)

For x = 1:

= > 2(1)³ + m(1)² + n(1) - 3 = 0

= > 2(1) + m(1) + n(1) - 3 = 0

= > 2 + m + n - 3 = 0

= > m + n - 1 = 0

= > m + n = 1 ... (1)

Adding (1) and (2):

= > ( m - n ) + ( m + n ) = 5 + 1

= > m - n + m + n = 6

= > 2m = 6

= > m = 6/2 = 3

And then,

= > m - n = 5

= > 3 - n = 5

= > 3 - 5 = n

= > - 2 = n

Answer 2

Answer:

If x+1 and x-1 are factors of 2x^3+mx^2+nx-3 , value of this polynomial must be 0, for x = -1, 1

➡ For x = -1:-

=> 2(-1)³ + m (-1)²+n(-1)-3= 0

=> 2(-1) + m(1)+n(-1)-3=0

=> -2+m-n-3 = 0

=> m-n = 5 = 0

=> m-n = 5 .....(I)

➡ For x= 1 :-

=> 2(1)³ +m(1)²-3 = 0

=> 2(1) + m(1) +n(1)-3 = 0

=> 2+ m +n-3 = 0

=> m+n-1 = 0

=> m+n = 1 .....(ii)

➡ Adding (I) and (ii).

=> (m-n)+ (m+n) = 5+1

=> m-n+m+n = 6

=> 2m = 6

=> m = 6/2 = 3

➡ And then,

=> m-n = 5

=> 3+n = 5

=> 3-5 = n

=> -2 = n

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