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Factor Theorem

If x3+kx2+m...

Question

If $x^{3} + k x^{2} + m x + 10 = (x + 1) (x - 2) (x - 5)$ then find the values of k and m.

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Solution

Given $x^{3} + k x^{2} + m x + 10 = (x + 1) (x - 2) (x - 5)$ on solving RHS simultaneously.
$x^{3} + k x^{2} + m x + 10 = (x + 1) (x^{2} - 7 x + 10)$
$x^{3} + k x^{2} + m x + 10 = x^{3} - 6 x^{2} + 3 x + 10$
on comparing LHS & RHS
we get [k=-6] and [m=3]
$∴ [k = - 6]$ and $[m = 3]$

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