If (x + 2) and (x - 1) are factors of the expression Lx + 2kx² + 24, find the values of L and k.

Correct Answer is : l = -12, k = -6

Correct Answer is : l = -12, k = -6

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JAMB Mathematics 2021 Paper

Question : 40

Total: 40

Lx + 2kx^{2} + 24

, find the values of L and k.

Solution:

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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