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# This question looks harder than it appears (quadratic) watch

1. Given that A and B are roots of the equation x^2+3x-6=0, find a quadratic equation with integer coefficients whose roots are 2/A and 2/B.

This is what I done so far:

Forgot what to do now
2. The question use sum and product surely

2/a +2/b = 2(a+b)/ab

2/a * 2/b = 4/ab

From the original

a+b = -3
ab = -6
3. (Original post by Prokaryotic_crap)
...
Your method of solving it is harder than it needs to be.

Recall a quadratic can be written as x^2-("sum of roots") x + "product of roots"=0

So, A+B = ..., AB=...

Now do the sum and product of roots for your new quadratic.
4. How about you just expand out ?
5. Try supposing that your expression is equal to (X-A)(X-B) and see what you can discover.
6. You don't need to solve A and B.

You should know facts about the roots of polynomials.

So write down A+B and AB.

Now consider

Can you rewrite this using A+B and AB?

Finally consider

Rewrite this using AB.

You will need to multiply the whole equation by 3 to obtain integer coefficients.
7. (Original post by Mr M)
You don't need to solve A and B.

You should know facts about the roots of polynomials.

So write down A+B and AB.

Now consider

Can you rewrite this using A+B and AB?

Finally consider

Rewrite this using AB.

You will need to multiply the whole equation by 3 to obtain integer coefficients.
ok, this is what I got:

correct?
8. (Original post by Prokaryotic_crap)
ok, this is what I got:

correct?
Look at the coefficient of x.

Remember the sum of the roots is
9. (Original post by Mr M)
Look at the coefficient of x.

Remember the sum of the roots is
Ftfy too late
10. Did anyone mention the substitution method?

If x^2+3x-6=0 has roots A and B then (2/u)^2+3(2/u)-6=0 has roots 2/A and 2/B.

Multiply through by u^2 to finish.
11. (Original post by BabyMaths)
...
Very nice - PRSOM.
12. (Original post by Mr M)
Look at the coefficient of x.

Remember the sum of the roots is
what do you mean? b = 3 a = 1 so -b/a = -3?
13. (Original post by Prokaryotic_crap)
what do you mean? b = 3 a = 1 so -b/a = -3?
Do you remember doing this in A Level Further Maths?

I'm talking about the second equation (the one you are forming). Your sign is wrong for the coefficient of x.
14. (Original post by Mr M)
Do you remember doing this in A Level Further Maths?

I'm talking about the second equation (the one you are forming). Your sign is wrong for the coefficient of x.
yh, i remember?

so, ?

I though the general form was ?

edit: Just spotted it!

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