```Question 64562
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<A<1

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