Q. 73.5( 47 Votes )

# If *x*+ 2 and *x* – 1 are the factors of *x*^{3} + 10*x*^{2} + *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) = x^{3}+10x^{2} +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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