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\right)\left(x - 5\right) \le 0

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

(a)2 marks

Find the root values that divide the real line into sign intervals

Lower critical value Upper critical value

(b)1 mark

Which sign description is valid on the real-line intervals?

positive when x<0, negative when 0<x<5, and positive when x>5

negative when x<0, positive when 0<x<5, and negative when x>5

State the solution topology for the given relation

Values of x below 0 or above 5, including both boundary values

Values of x between 0 and 5, including both boundary values

No real value of x

Every real value of x

(d)2 marks

List the relevant finite boundary values exactly

Lower finite boundary Upper finite boundary

(e)1 mark

Select the correct inclusion statement

Include the finite boundary values in the solution

Exclude the finite boundary values from the solution

There are no finite boundary values to include