What is this question asking? Find all real x such that x^6 - 3x^3 - 10 = 0

[triangle4]

On my review for my exam for tomorrow I have this question:
Find all real numbers x such that [imath]x^6 - 3x^3 - 10 = 0[/imath]

I cant ask my professor because he is unavailable (as are my classmates).

What is it asking for?
Is it asking for the domain (which is all real numbers)?
Or is it asking for the roots?

 

[topsquark]

On my review for my exam for tomorrow I have this question:
Find all real numbers x such that [imath]x^6 - 3x^3 - 10 = 0[/imath]

I cant ask my professor because he is unavailable (as are my classmates).

What is it asking for?
Is it asking for the domain (which is all real numbers)?
Or is it asking for the roots?

Hint: Change of variables. Let [imath]y = x^3[/imath]. Then your equation is [imath]y^2 - 3y - 10 = 0[/imath].

Can you finish?

-Dan

 

[lev888]

On my review for my exam for tomorrow I have this question:
Find all real numbers x such that [imath]x^6 - 3x^3 - 10 = 0[/imath]

I cant ask my professor because he is unavailable (as are my classmates).

What is it asking for?
Is it asking for the domain (which is all real numbers)?
Or is it asking for the roots?

Yes, it's asking for the roots, because the roots are the real numbers that satisfy the equation. A domain is a property of a function, not of an equation.

 

[stapel]

On my review for my exam for tomorrow I have this question:
Find all real numbers x such that [imath]x^6 - 3x^3 - 10 = 0[/imath]

I cant ask my professor because he is unavailable (as are my classmates).

What is it asking for?
Is it asking for the domain (which is all real numbers)?
Or is it asking for the roots?

It didn't ask you to "Find the domain of the polynomial [imath]f(x) = x^6 - 3x^3 - 10[/imath]"

It asked you to "Find all...[imath]x[/imath] such that [the polynomial] is equal to zero". So it is asking you to find the solution values [imath]x[/imath] for [the polynomial].

So factor the polynomial (which is quadratic in form), set each factor equal to zero, apply the formulas for factoring sums and differences of cubes, and then solve each of the factors. (Only two of the four factors will have real-valued roots.)