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Question
If x + 2 and x − 1 are the factors of x3 + 10x2 + mx + n, then the values of m and n are respectively
Options
5 and −3
17 and −8
7 and −18
23 and −19
Solution
It is given (x + 2)and (x - 1)are the factors of the polynomial
`f(x) = x^3 + 10x^2 + mx + n`
i.e., f(-2) =0 and f(1) = 0
Now
`f(-2) = (-2)^3 + 10(-2)^2 + m(-2) + n =0`
\[- 8 + 40 - 2m + n = 0\]
\[ \Rightarrow - 2m + n = - 32\]
\[ \Rightarrow 2m - n = 32 . . . (1)\]
`f(1) = (1)^3 + 10(1)^2 +m(1) + n = 0`
`1 + 10 +m + n = 0`
` m + n = -11 ........ (2)`
Solving equation (1) and (2) we get
m = 7 and n = − 18
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