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# Roots of equation watch

1. The roots of the equation :

where k is real constant ,are denoted by &

a) Show that the equation whose roots are

&

is

I tried

and ended up with
also in the initial equation given it factorises to a perfect square

I cant see what to do next , any hints in the right direction will be helpful thanks
2. Do you know about the relationships between the roots of equations and the coefficients of a quadratic equation?

For the equation ax^2+bx+c=0

A + B = -b/a
A*B=c/a
(where A and B are roots)

Put the first equation in the form ax^2+bx+c=0 and see if this gets you anywhere...
3. There is a standard process for this type of question.

Suppose ax^2 + bx + c = 0 has two roots p and q

Then p+q = -b/a and pq = c/a

If you then want to construct new equation with 1/p and 1/q, you can quickly see that product of roots of this new equation = 1/pq.

After a bit of faff you can work out (1/p) + (1/q) in terms of p+q and pq, which you know from initial equation.

So you now know sum-of-roots and product-of-roots for new equation.

So you can construct your new equation.
4. (Original post by ian.slater)
There is a standard process for this type of question.

Suppose ax^2 + bx + c = 0 has two roots p and q

Then p+q = -b/a and pq = c/a

If you then want to construct new equation with 1/p and 1/q, you can quickly see that product of roots of this new equation = 1/pq.

After a bit of faff you can work out (1/p) + (1/q) in terms of p+q and pq, which you know from initial equation.

So you now know sum-of-roots and product-of-roots for new equation.

So you can construct your new equation.
sorry but thats what I have done

I multiplied through alphabeta .. however I think now you put it that way I understand what to do now ..the only think thats troubling me is the 4kx ?
5. You could have done x = 1/a, so a = 1/x, then replaced for x and multiplied out.

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