Q. 73.5( 47 Votes )

If x+ 2 and x – 1 are the factors of x3 + 10x2 + mx + n, the find the value of m and n.

Answer :

Concept Used:


Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0


Explanation:


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


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