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

Assessment: JAMB UTME - Mathematics - 2021 Subject: General Mathematics

Question 1 Report

l = -12, k = -6

l = -2 , k = 1

l = -2 , k = -1

l = 0, k = 1

Answer Details

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 = $f r a c - 72 12$

k = -6

where L = -24 - 2k

L = -24 - 2(-6)

L = -24 + 12

L = -12

That is; K = -6 and L = -12

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