Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
As zÂ² - 4z - 5 is the kind of a*x^2 + b*x + c where a is positive, thus (z-1)(z+5) > 0 is possible when z is not between the 2 roots : -1 and 5.
Hence, we know that z < -1 or z > 5
The question is a bit strange.... we cannot be sure here ... But as we have to choose, I take (E)
I get: z^2-4z-5>0 (z-5) (z+1)>0 z>5,z>-1
I do not understand the change in sign part. Pls explain.
We apply this rule :
> f(x) = a*x^2 + b*x + c where a is positive, f(x) > 0 when x is not between its roots if these roots exist.
> f(x) = a*x^2 + b*x + c where a is negative, f(x) > 0 when x is between its roots if these roots exist.
If we represent f(z)=z^2-4z-5 in XY plan, we obtain the fig1.
I also add u the representation of g(z)=-z^2-4z+5 to have the case with a <0 in the fig2.
Fig1_a-postive.jpg [ 17.01 KiB | Viewed 506 times ]
Fig2_a-negative.jpg [ 16.88 KiB | Viewed 505 times ]
I got E for this one. My question is why is it this question an odd one ?? examining other choices, only x<-1 is one of the two solution. the other solution which is x>5 is not there and x> -5 or x>-1 range is too wide to make x always true.