How to continue this question?

[Kulla_9289]

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.

 

[Dr.Peterson]

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.

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]

Or writing the equation as (x-a)^2(x-b)^2 = 0?

Why? What's the logic?

 

[Dr.Peterson]

Why? What's the logic?

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.

 

[Kulla_9289]

Yeah, I was able to prove it. Thanks for the help.

 

[khansaheb]

we get: 2a + 2b

How is that?

Why? What's the logic?

Two pairs of real roots are equal (op)

 

[khansaheb]

How is that?


Two pairs of real roots are equal (op)

However I am not sure what does that mean! In normal English two pairs would mean 4 (= 2 * 2)