How do you solve #z^2-5z-7<0# using a sign chart?

1 Answer
Dec 27, 2017

Answer:

Solution: # -1.14 < z < 6.14#

Explanation:

#z^2-5z-7=0 or z^2-5z=7# or

#(z^2-5z+2.5^2)=7+2.5^2 or (z-2.5)^2=13.25# or

#(z-2.5)=+-sqrt 13.25 or z= 2.5+-sqrt13.25#

#:. z~~ 6.14 , z ~~ -1.14 :.#

#z^2-5z-7 <0 or (z-6.14)(z+1.14)<0#

Critical numbers are # z~~ -1.14 , z ~~ 6.14 #

Sign chart:

When #z< -1.14# sign of #(z-6.14)(z+1.14) # is # (-) * (-) = (+) ; >0 #

When # -1.14 < z < 6.14# sign of #(z-6.14)(z+1.14) # is # (-) * (+) = (-) ; < 0#

When # z > 6.14 # sign of #(z-6.14)(z+1.14) # is # (+) * (+) = (+) ; > 0#

Solution: # -1.14 < z < 6.14#

graph{x^2-5x-7 [-40, 40, -20, 20]} [Ans]