A level further maths help!!!Watch
The new equation will have roots and .
So, this means the new equation will be
Your goal is to express and in terms of and because you know those from part (a) and so you can just sub those numbers in and simplify the coefficients to nice numbers!
Obviously, the constant term is just 1 so we don't even need to work on this one.
But for you want to first combine it into a single fraction and the denominator is already good for us. Just deal with the numerator... what's in terms of and ??
Same approach to all questions.
So we can work in reverse, we know the brackets will be . So you can expand this out to get the equation.
You should probably stick your values for alpha and beta in before you expand, otherwise it'll get messy. Then once you expand these brackets you'll arrive at a quadratic that has those roots, and you know this because at the start you put these as the roots.
If a quadratic has roots and then you can work in reverse. What I mean by this is for example has roots 4 and 1, we know this by factorising to get
Instead, if we consider the new roots to be and , we need only find and to be able to write down the new quadratic.
Since we can rewrite to get , all we really need to do is the (hopefully familiar by now) calculation to find in terms of and . The calculation of is even easier (once you've found \gamma+\delta).