Question
Find the interval(s) in which the expression (4-x)(x+2) is positive.
Answer: Option B
:
B
LetP=(4−x)(x+2)
Find the points on the number line where P=0
P=0⇒xϵ{−2,4}
Split the number line into 3 using these points.
(−∞,−2),(−2,4)&(4,∞)(−∞,−2):(4−x)>0&(x+2)<0⇒P<0(−2,4):(4−x)>0&(x+2)>0⇒P>0(4,∞):(4−x)<0&(x+2)>0⇒P<0
∴P>0,whenxϵ(−2,4)
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:
B
LetP=(4−x)(x+2)
Find the points on the number line where P=0
P=0⇒xϵ{−2,4}
Split the number line into 3 using these points.
(−∞,−2),(−2,4)&(4,∞)(−∞,−2):(4−x)>0&(x+2)<0⇒P<0(−2,4):(4−x)>0&(x+2)>0⇒P>0(4,∞):(4−x)<0&(x+2)>0⇒P<0
∴P>0,whenxϵ(−2,4)
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