If (x + 2) and (x - 1) are factors of the expression \(Lx + 2kx^{2} + 24\), find the values of L and k.
Given (x + 2) and (x - 1), i.e. x = -2 or +1
when x = -2
L(-2) + 2k(-2)\(^2\) + 24 = 0
f(-2) = -2L + 8k = -24...(i)
And x = 1
L(1) + 2k(1) + 24 = 0
f(1):L + 2k = -24...(ii)
Subst, L = -24 - 2k in eqn (i)
-2(-24 - 2k) + 8k = -24
+48 + 4k + 8k = -24
12k = -24 - 48 = -72
k = \(frac{-72}{12}\)
k = -6
where L = -24 - 2k
L = -24 - 2(-6)
L = -24 + 12
L = -12
That is; K = -6 and L = -12
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