I have done part i of the attached question. Do I have to understand complex numbers for part ii?
Hello Stuck Man
It looks as if you don't know about this important result:
- If and are the roots of the quadratic equation , then:
(This is very easy to prove: expand and compare it to .)The sum of its roots,andThe product of its roots,
Well then, if and are the roots of , we get:and
So for part (i):
Now substitute in the values of and , simplify and the job's done. (I get the answer . Do you agree?)
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Part (ii)
We know the value of and clearly . So we can use the result in reverse to write down the new equation, knowing the sum and product of its roots; i.e.which (if my arithmetic is correct) is:
i.e.
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Part (iii)
is a root of . So:Grandad
(1)
from (1)