2021
Mathematics
67ca00ce0c643c71d77dee1f
If (x + 2) and (x - 1) are factors of the expression Lx+2kx2+24 , find the values of L and k.
A.
l = -12, k = -6
B.
l = -2 , k = 1
C.
l = -2 , k = -1
D.
l = 0, k = 1
Correct Answer: l = -12, k = -6
Explanation
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 = −72/12 k = -6 where L = -24 - 2k L = -24 - 2(-6) L = -24 + 12 L = -12 That is; K = -6 and L = -12
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 = −72/12 k = -6 where L = -24 - 2k L = -24 - 2(-6) L = -24 + 12 L = -12 That is; K = -6 and L = -12THIS WEEK's
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