Question

if (x+2) and (x+1) are the factors of x^3+10x^2+mx+n. find the value of M and N

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:- The value of m and n is 23 and 14.

Step by step explanation:-

Given:- (x+2) and (x+1) are the factors of x^3+10x^2+mx+n.

To find:- the value's of m and n.

Solution:-

(x+2) and (x+1) are the factors

hence, x= -2 and x= -1

Putting the values in x^3+10x^2+mx+n

Let x= -2

(-2)^3 + 10(-2)^2 + m(-2) + n =0

-8 + 40 -2m + n =0

-2m + n + 32 =0-------(1)

Now, Let x= -1

(-1)^3 + 10(-1)^2 + m(-1) + n =0

-1 +10 -m + n =0

-m + n + 9 =0--------(2)

Equation (2) can be written as

n=m-9

Putting the value of n in equation (1)

-2m + m - 9 + 32 =0

-m + 23=0

m = 23

Now, Putting the value of m in equation (2)

-m + n + 9 =0

-23 + n + 9 =0

n - 14 =0

n = 14

The value of m and n is 23 and 14.

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