Polynomial Help! (1 Viewer)

[cyndix3]

Hi, having troubles solving this:


If the polynomial x³ + 3px² + 3qx + r = 0.
Show that the double roots must be (pq - r)/(2q - p²)





Thanx heaps in advance!

 

[ohexploitable]

 

[Bored Of Fail 2]

your working looks correct, cant find any algebra mistakes

 

[jyu]

your working ok, (pq - r)/(2(q - p²))

 

[khfreakau]

Algebra might get a little ugly, but what I'd do is sub (pq-r)/(2q-p^2) as x in each equation, and show that =0. By doing that, you're "showing" that it's a root of P(x) and P'(x). To be safe, I'd also sub it into P''(x) and show that it's not a root of that to show that it's definitely a double root. A more surefire method, imo.

 

[cutemouse]

Algebra might get a little ugly, but what I'd do is sub (pq-r)/(2q-p^2) as x in each equation, and show that =0. By doing that, you're "showing" that it's a root of P(x) and P'(x). To be safe, I'd also sub it into P''(x) and show that it's not a root of that to show that it's definitely a double root. A more surefire method, imo.

+1

 

[ttrinix]

Algebra might get a little ugly, but what I'd do is sub (pq-r)/(2q-p^2) as x in each equation, and show that =0. By doing that, you're "showing" that it's a root of P(x) and P'(x). To be safe, I'd also sub it into P''(x) and show that it's not a root of that to show that it's definitely a double root. A more surefire method, imo.

+1
Algebra bashing is only required if you need to "Find an expression for the double root"

 

[ohexploitable]

Algebra might get a little ugly, but what I'd do is sub (pq-r)/(2q-p^2) as x in each equation, and show that =0. By doing that, you're "showing" that it's a root of P(x) and P'(x). To be safe, I'd also sub it into P''(x) and show that it's not a root of that to show that it's definitely a double root. A more surefire method, imo.

+1

+1
Algebra bashing is only required if you need to "Find an expression for the double root"

lol, have fun guys.

 

[deterministic]

^ +1