Question

find the value of m and n if (x+2) and (x+1) are factors of x power 3 +3x power 2-2mx+n

Answer 1

Heya !!!

Given that,

( X +2) as well as ( X +1) are the factor of the given polynomial.

Therefore,

( X +2) = 0 And ( X +1) = 0

X = -2 And X = -1

P(X) = X³ + 3X² - 2MX + N

P(-2) = (-2)³ + 3 × (-2)² - 2 × M × -2 + N

=> -8 + 3 × 4 + 4M + N = 0

=> 4M + N + 8 -12 = 0

=> 4M + N = -4 ----------(1)

Also,

X = -1

P(-1) = (-1)³ + 3 × (-1)² - 2M × -1 + N

=> -1 + 3 + 2M + N => 0

=> 2M + N + 2 = 0

=> 2M + N = -2 --------(2)

From equation (1) we get,

4M + N = -4

N = -4 - 4M --------(3)

Putting the value of N in equation (2)

2M + N = -2

2M + ( -4 - 4M ) = -2

2M -4 - 4M = -2

-2M = -2+4

-2M = -2

M = 2/2

M = 1

Putting the value of M in equation (3)

N = 2 - 4M = 2 - 4 × 1

N = 2 - 4

N = -2

Hence,

M = 1 and N = -2

Answer 2

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