How to continue this question?

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Kulla_9289

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I started my working by writing down all the possible roots: a, b, c, d. Since two pairs are the same, we get: 2a + 2b. Using the sum of roots of formula, we get zero, so on equating 2a + 2b=0, a+b=0. And now I am not sure on how to continue? Any guidance is appreciated.
 
Kulla_9289 said:
View attachment 38598
I started my working by writing down all the possible roots: a, b, c, d. Since two pairs are the same, we get: 2a + 2b. Using the sum of roots of formula, we get zero, so on equating 2a + 2b=0, a+b=0. And now I am not sure on how to continue? Any guidance is appreciated.
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Have you tried using the other formulas relating roots to coefficients?

Or writing the equation as (x-a)^2(x-b)^2 = 0?
 
Kulla_9289 said:
Why? What's the logic?
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Generally, the way to find out whether something helps is to try it.

Expand the expression and match it up to the coefficients of the polynomial. This is actually how Vieta's formulas are derived, but applied to the special case so that there is less to do. The other approach is therefore a little quicker, but this is easier if you forgot the formulas.

But if you first apply the observation you already made, the work becomes almost trivial.
 
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