1 of 8 0-day streak

Analyse signs and solve a quadratic inequality

Question 1 of 8

No calculator

Consider the following quadratic inequality over the real numbers

\left(x + 6\right)\left(x + 1\right) < 0

Use exact values. Analyse the sign of the left side after it has been compared with zero

(a)2 marks

Determine the real values at which the left side is zero

Lower critical value Upper critical value

(b)1 mark

Select the correct sign pattern separated by the real roots

negative when x<-6, positive when -6<x<-1, and negative when x>-1

positive when x<-6, negative when -6<x<-1, and positive when x>-1

Select the interval pattern for the solution set

Values of x below -6 or above -1, excluding both boundary values

Every real value of x

No real value of x

Values of x between -6 and -1, excluding both boundary values

(d)2 marks

Which root values are the finite endpoints of the solution intervals?

Lower finite boundary Upper finite boundary

(e)1 mark

Choose the correct endpoint convention for the relation

Include the finite boundary values in the solution

There are no finite boundary values to include

Exclude the finite boundary values from the solution