f(x) = k has exactly two roots, state the range of possible values of k

[David79865]

Hi there,

I don't understand following exercise:
given the equation f(x) = k, where k is a constant, has exactly two roots, state the range of possible values of k
What exactly am I supposed to find out? And how?
Until now, I only saw things like
f(x) = 2k^2 + k - 3 , find the range of values for that k has real roots
Then I would use (-b +- sqrt(b^2-4ac))/(2a) -> b^2 - 4ac >= 0 and solve it like this.

So to have exactly two roots, b^2 - 4ac must be greater than 0. But I don't even have a quadratic funtction, so I'm really confused.

Thanks for all your help!

 

[Deleted member 4993]

Hi there,

I don't understand following exercise:
given the equation f(x) = k, where k is a constant, has exactly two roots, state the range of possible values of k
What exactly am I supposed to find out? And how?
Until now, I only saw things like
f(x) = 2k^2 + k - 3 , find the range of values for that k has real roots
Then I would use (-b +- sqrt(b^2-4ac))/(2a) -> b^2 - 4ac >= 0 and solve it like this.

So to have exactly two roots, b^2 - 4ac must be greater than 0. But I don't even have a quadratic funtction, so I'm really confused.

Thanks for all your help!

"...the equation f(x) = k, where k is a constant, has exactly two roots, state the range of possible values of k..."

If this the EXACT problem statement - then this function f(x) cannot have exactly two roots.

Your thought process is correct.

 

[HallsofIvy]

The question does not ask for roots of the function, f(x), it asks for roots of the equation, f(x)= 0.