Question

If (x+1) and (x-2) are factor of the polynomial x cube + mx square +2x+n find the value of m and n

Answer 1

we have (x+1) is a factor

then x=-1

now put 1 in the equation

we get

${x}^{3} + m {x}^{2} + mx + 2x + n \\ \\ after \: putting \: - 1we \: get \\ - 1 + m - m - 2 + n = 0 \\ - 3 + n = 0$

now take 2 as a factor

we get

$12 + 6m + n = 0$

equating both the equations

we get

$- 3 + n = 12 + 6m + n \\ 9 + 6m = 0 \\ m = \frac{ - 3}{2}$

then n will be

$n = - 3$

that's your answer hope you like this

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