$If x + 2 and x - 1 are the factors of x^{3} + 10 x^{2} + m x + n, then find the values of m and n respectively.$

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Solution

$Here, x + 2 is a factor of x^{3} + 10 x^{2} + m x + n$

$x = - 2$

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

$- 8 + 40 = 2 m - n$

$2 m - n = 32 . . . . . (i)$

Again for x-1

$x = 1$

$1 + 10 + m + n = 0$

$m + n = - 11 . . . . . (i i)$

Adding (i) and (ii). we get,

$3 m = 21$

$m = 7$

By putting m in (i). we get,

$2 (7) - n = 32$

$- n = 18$

$n = - 18$

$So, m = 7 and n = - 18$

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If x+2 and x−1 are the factors of x3+10x2+mx+n, then find the values of m and n respectively.

Here, x+2 is a factor of x3+10x2+mx+n x=−2 (−2)3+10(−2)2+m(−2)+n=0 −8+40=2m−n 2m–n=32.....(i) Again for x-1 x=1 1+10+m+n=0 m+n=−11.....(ii) Adding (i) and (ii). we get, 3m=21 m=7 By putting m in (i). we get, 2(7)−n=32 −n=18 n=−18 So, m=7 and n=−18

$If x + 2 and x - 1 are the factors of x^{3} + 10 x^{2} + m x + n, then find the values of m and n respectively.$