How do you solve and write the following in interval notation: #x^2-1x-30>0#?

1 Answer
Binayaka C.
Apr 14, 2017

Solution : # x <-5 or x >6 #. In interval notation: #(-oo , -5) uu (6,oo)#.

Explanation:

#x^2-x-30 >0 or x^2-6x+5x-30 >0 or x(x-6) +5(x-6) >0 or (x+5)(x-6)>0#
Critical points are #x = -5 , x =6 #

When # x < -5; (x+5)(x-6) is (-)*(-) = (+) or >0 #

When # -5< x < 6; (x+5)(x-6) is (+)*(-) = (-) or <0 #

When # x > 6; (x+5)(x-6) is (+)*(+) = (+) or >0 #

Solution : # x <-5 or x >6 #. In interval notation: #(-oo , -5) uu (6,oo)#. The graph also confirms the findings. graph{x^2-x-30 [-80, 80, -40, 40]}[Ans]

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