Roots Of Polynomials

Question 1

MUST MAKE SURE

Answer 1

You check all your roots exact, if not exact small error

Nor remember even one root might be correct other wring so have to go agsin

Question 2

How to do if now root is alpha sqaured?

Answer 2

Z is now z ^0.5

Now out that in

Now might have to sqaure eveyrhignf at the end to make it even power numbers

Can be easier if move half to the right and keep half on the left, less chance of making mistake

Now rearrange and CHECK

Question 3

How to prove complex number a root?

Answer 3

Use fsctor theroem and sub inside should give 0!

Question 4

If they give you two complex roots and some more info, how to best find all the other roots?

It’s a quart IV

Answer 4

Basically expand the two complex roots, then work out by inspection what the other numbers will have to be of the other quadratic thst multiplies with this one you made

Do this by looking st info in a, look at linear terms etc. Put a CONSTANT down for anything you cantfind

Now expand and equate to a number you know

Once you found CONSTSNT it become shells easy after that to solce