# Algebra question?

##
#f(x)=x^3-x^2-x-(11/4).#

If #k# is a constant such that the equation #f(x)=k# has three real solutions, what could be the value of #k# ?

If

##### 1 Answer

#### Explanation:

(I have included steps that could be skipped ...e.g. this can be solved quickly by graphing, or eqns can be evaluated in one step with a calculator.

Hopefully this helps in understanding each step, although it looks a bit long).

If we graph this function we can see where the values for

graph{x^3-x^2-x-2.75 [-10, 10, -5, 5]}

If the value of

At the inflection points the **slope** of

so if we solve for

Use a the quadratic formula

put theses into

at

evaluate this now, or simplify the fractions:

or

So **at** these values).