Question

If x+2 and x-1 are the factors of x³ + 10x² + mx + n, then the value of m and n are respectively 

A. 5 and -3 

B. 17 and -8 

C. 7 and -18 

D. 23 and -19

Answer 1

Let f (x) = x³ + 10x² + mx + n 

Since, (x + 2) and (x - 1) are factor of f (x) 

So, 

f (-2) = 0 

(-2)³ + 10 (-2)² + m (-2) + n 

32 - 2m + n = 0 (i) 

f (1) = 0 (1)³ + 10 (1)² + m (1) + n = 0 

11 + m + n = 0 (ii) 

(2) - (1) 

3m -21 = 0 

m = 7 (iii) 

Using (iii) and (ii), we get 

11 + 7 + n= 0 

n = - 18