If (x + 2) and (x - 1) are factors of the expression \(Lx + 2kx^{2}...

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

There is an explanation video available below.

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