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Question 64562: I need help with 4 problems that I,m stuck on, its not in my book. 1. (x-8)(x+4)>0 2. (a+5)(a-1)(a-6)>0 3. 9x+x(x-8)=0 4. p^2-12p+35>0
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I need help with 4 problems that I,m stuck on, its not in my book.
1. SAY Y=(x-8)(x+4)>0
LET ME GIVE YOU THE METHOD USING NUMBER LINE PROCEDURE.
1.WRITE THE INEQUALITY AS AN EQUALITY....THAT IS
Y=(X-8)(X+4)=0
2.FIND THE ROOTS
X-8=0......X=8
X+4=0.......X=-4
THE 2 ROOTS ARE 8 AND -4
3.WRITE THE ROOTS IN AN INCREASING ORDER
-4,8
4.DRAW A NUMBER LINE FROM -INFINITY TO PLUS INFINITY AS BELOW
-INFINITY|____________________________________________________|+INFINITY
5.LOCATE THE 2 ROOTS ON THE LINE.AS SHOWN
-INFINITY|___________________________________________________|+INFINITY
..............................-4....................8..................
6.START FROM RIGHT MOST OR BIGGEST ROOT.....X=8 HERE
7.Y IS +VE IN THE ZONE FROM THIS TO +INFINITY..THAT IS X=+8 TO +INFINITY...Y>0
8.TRAVEL LEFT TO THE NEXT ROOT...THAT IS FROM X=8 TO -4.IN THIS ZONE Y IS -VE.
9.TRAVEL FURTHER LEFT TO THE NEXT ROOT.IN THIS ZONE Y WILL BE AGAIN +VE. ..THERE ARE NO MORE ROOTS HERE.HENCE SKIP TO 11.
10.CONTINUE LIKE THIS FROM ONE ROOT TO THE OTHER.IN THESE ZONES Y WILL ALTERNATE FROM +VE TO -VE TO +VE TO -VE....ETC..
11.AFTER THE LAST ROOT GO TO -INFINITY.Y WILL BE +VE OR -VE DEPENDING ON THE SIGN IN THE PREVIOUS ZONE.HERE IN THE PREVIOUS ZONE OF X=-4 TO 8.. Y IS -VE.HENCE FROM -4 TO -INFINITY Y WILL BE +VE.
12. ANSWER .....Y IS POSITIVE FOR X>8 AND X<-4
FOLLOW THE SAME METHOD AND TRY THE OTHERS .IF IN STILL DIFFICULTY PLEASE COME BACK
2. Y=(a+5)(a-1)(a-6)>0
ANSWER...Y WILL BE +VE FOR A>6 AND -5
3. 9x+x(x-8)=0
FACTORISE..
9X+X^2-8X=0
X^2+X=0
X(X+1)=0
X=0....OR....X=-1
4. Y=p^2-12p+35>0
FACTORISE
(P-5)(P-7)>0
ANSWER
Y WILL BE +VE FOR P>7 AND P<5
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