1. ## intercepts

$x^4-6x-8$

y = -8

can't work out x intercepts.
Can anyone help?

2. Originally Posted by el123
$x^4-6x-8$

y = -8

can't work out x intercepts.
Can anyone help?
I assume your question is solve $x^4 - 6x - 8 = 0$. Here you go: Wolfram|Alpha

3. Ive tried that site already , it gives me an enormous equation.

Is there no simple way to find the x intercepts for that equation? Im trying to graph it. I need to do it algebraically but keep coming up with wrong answers.

4. Originally Posted by el123
Ive tried that site already , it gives me an enormous equation.

Is there no simple way to find the x intercepts for that equation? Im trying to graph it. I need to do it algebraically but keep coming up with wrong answers.
There is a process that can be followed for solving any quartic equation. You should realise from the complicated form of the answers that the solution process will be even more complicated. Why do you need exact answers, anyway. In situations like this, surely decimal approximations are sufficient.

5. well i want to know how to do it , I was asked to find max , min , points of inflection etc , then to graph it. I'm not going to be able to use the internet in the middle of an exam so i am thinking it would be helpful to learn how to do it myself instead of just reading the answers of a webpage.

We haven't covered quartic equations yet so i dont even know how to do it .No wonder i can't work it out, i did'nt even know it was one.lol

6. Originally Posted by el123
well i want to know how to do it , I was asked to find max , min , points of inflection etc , then to graph it. I'm not going to be able to use the internet in the middle of an exam so i am thinking it would be helpful to learn how to do it myself instead of just reading the answers of a webpage.

We haven't covered quartic equations yet so i dont even know how to do it .No wonder i can't work it out, i did'nt even know it was one.lol
What you want to do is ludricous. Surely you can see that.

Where has this particular equation come from and what makes you think it has to be solved exactly?

7. It is in my weekly assignment.

''4. Find the maximum and/or minimum values and any points of inflexion of the
function $x^4-6x-8$ . Sketch the curve by using this and any other needed
information.
''

Ive worked out everything but the x intercepts.

8. Originally Posted by el123
It is in my weekly assignment.

''4. Find the maximum and/or minimum values and any points of inflexion of the
function $x^4-6x-8$ . Sketch the curve by using this and any other needed
information.
''

Ive worked out everything but the x intercepts.
you can sketch the curve without knowing the exact values of the x-intercepts.

understand that a sketch reflects the general shape of the graph.

I appreciate your desire to know how to solve such equations, but as stated by Mr. F, you must realize that some equations cannot be solved using elementary algebraic principles.

9. Thats cool , i wasn't aware it was such a complicated equation. Thanks to both of you for the replies.

and this one too,
''4. Find the maxi
mum and/or minimum values and any points of inflexion of the function . Sketch the curve by using this and any other needed information.''

What is that y = -8 for? x - intercept?

i just wonder about that y = -8 THING, thanks

11. ## graph

see this

12. Originally Posted by pacman

and this one too,
''4. Find the maxi
mum and/or minimum values and any points of inflexion of the function . Sketch the curve by using this and any other needed information.''

What is that y = -8 for? x - intercept?

i just wonder about that y = -8 THING, thanks
I assume y = -8 is the y-intercept.

13. so then, the equation might be y = x^4 - 6x - 8?

@ x = 0, y = (0)^4 - 6(0) - 8 = -8

Now, i get it.

To get the x-intercept, set y = 0.

0 = x^4 - 6x - 8.

Solving for the roots,

x1 = -1.094;

x2 = 2.136;

x3 = -0.52 - 1.76i;

x4 = -0.52 + 1.76i

Thanks Mr Fantastic.