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

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

Answer Details

Given (x + 2) and (x - 1), i.e. x = -2 or +1

when x = -2

L(-2) + 2k(-2)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−7212 $frac-7212$

k = -6

where L = -24 - 2k

L = -24 - 2(-6)

L = -24 + 12

L = -12

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