How do you solve and write the following in interval notation: #x^2 + 6x + 5 >= 0#?

1 Answer
Narad T.
Nov 7, 2016

The interval notation is #] -oo,-5 ] uu [-1,+oo[#

Explanation:

Let's factorise the equation
#y=x^2+6x+5>=0# #=>##(x+1)(x+5)>=0#
Let's do a sign chart
#color(white)(aaaa)##x##color(white)(aaa)##-oo##color(white)(aaaa)##-5##color(white)(aaa)##-1##color(white)(aaa)###+oo #color(white)(aa)##x+5##color(white)(aaaaaaa)##-##color(white)(aaa)##+##color(white)(aaa)##+##color(white)(aaa)#
#color(white)(aa)##x+1##color(white)(aaaaaaa)##-##color(white)(aaa)##-##color(white)(aaa)##+##color(white)(aaa)#
#color(white)(aaaaa)##y##color(white)(aaaaaaa)##+##color(white)(aaa)##-##color(white)(aaa)##+##color(white)(aaa)#

So #y>=0# on the intervals # ] -oo,-5 ] uu [-1,+oo[#
graph{x^2+6x+5 [-10.8, 5.004, -5.31, 2.59]}

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