Thread: Polynomial questions

I tried doing these, but I always got the wrong answer or just got stuck on one part.

1.Resolve algebraically

I have absolutely no clue on how to start with this one.
2.
I squared both sides, but it kept getting more and more complicated and really confused me.

3.Determine the coordinates of the intersection points between the line and the circle

I tried substituting the line into the circle equation, but than I didn't know where to go from there.

Thanks guys.

Originally Posted by Methodd

I tried doing these, but I always got the wrong answer or just got stuck on one part.

1.Resolve algebraically

I have absolutely no clue on how to start with this one.

Hint: factor

2.
I squared both sides, but it kept getting more and more complicated and really confused me.

Hint: rewrite as
Now square both sides.

3.Determine the coordinates of the intersection points between the line and the circle

I tried substituting the line into the circle equation, but than I didn't know where to go from there.

Yes, your approach is correct. What did you get after substituting? Simplify, and you should have a quadratic equation.

Yes, your approach is correct. What did you get after substituting? Simplify, and you should have a quadratic equation.

I got

Careful! I think you've made the mistake of square rooting both sides. You can't do that here because
Let and to prove this quite simply yourself.

Anyway, going back to your question:

Substituting that into gives:




Do not square root here.
You have to expand the brackets.

Tidy from here and factorize - you get a nice answer.

Thanks guys, that really helped!