Question

5. If x+2 and x-1 are the factors of x^3+10x^2+mx+n, then the values of mand n are respectively
(a) 5 and - 3
(b) 17 and - 8
(c) 7 and -18
(d) 23 and -19​

Answer 1

Answer:

n=−18

Option C is correct

Answer 2

Answer:

( c ) 7 and -18

Given that ;

Factors :

• x + 2

Hence ;

x = -2

• x - 1

Hence ;

x = 1

x³ + 10x² + mx + n = 0

Substitute x value as 1 ;

1 + 10 + m + n = 0

11 + m + n = 0

m + n = -11 ---- ( 1 )

Substitute x value as -2 ;

x³ + 10x² + mx + n = 0

- 8 + 40 - 2m + n = 0

32 - 2m + n = 0

32 = 2m - n

2m - n = 32

2m - n = 16 ----- ( 2 )

Elimination Method :

m + n = -11

2m - n = 32

----------------

3m = 21

m = 21 / 3

m = 7

Substitute m value in the Equation ( 1 ) ;

m + n = -11

7 + n = -11

n = - 11 - 7

n = -18