If z² - 4z > 5 then which of the following is always true
A) z > -5
B) z < 5
C) z > -1
D) z < 1
E) z < -1
IfIf z² - 4z > 5 then which of the following is always true
(z-5)(z+1)>0 or ab>0
there are two cases either a>0 and b>0 or a<0 and b<0
Now question does not end here we have to take into consideration the resulting values with our equation
we get z>-1and z>5 or z<-1 and z<5
here z>5 and z<-1 fits the criteria
hence the solution
There is no correct answer.
z² - 4z > 5
z² - 4z - 5 > 0
(z - 5)(z + 1) > 0
Two possibilities: the two factors (z - 5) and (z + 1) are either both positive or both negative. In other words, either z > 5 or z < -1. Plug any number that is greater than 5 or any number that is less than -1 into z² - 4z and you will get a value greater than 5. For example, if z = 6, then z² - 4z = 12, which is greater than 5. Or, if z = -6, then z² - 4z = 60, which is greater than 5.
Now, the question asks "which of the following is always true?"
That z could be -6 proves than neither (A) nor (C) is necessarily true.
That z could be 6 proves that neither (B) nor (D) nor (E) is necessarily true.
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