Please Help With This Maths Question (1 Viewer)

[star*eyed]

The polynomial equation p(x) = 0 has the double root at x=a. By writing p(x) = (x-a) <SUP>2 </SUP>Q(x), where Q(x) is a polynomial, show that P<SUP>l</SUP><SUP> </SUP>(a) = 0

****THe dash next to the P means derivarive***<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>

 

[pLuvia]

Well this is basic 4 unit polynomials so here it goes.

If P(x)=0 has a double root, x=a this means P'(a)=0

P(x)=(x-a)²Q(x)
P'(x)=2(x-a)Q(x)+(x-a)²Q'(x)
.: P'(a)=0

QED

 

[star*eyed]

Hey thanx for the help, but im still really confused. I only do 3 unit!

 

[pLuvia]

By writing p(x) = (x-a) 2 Q(x), where Q(x) is a polynomial, show that Pl(a) =0

Well it tells you the equation you will need to differentiate so when you differentiate you get

P'(x)=2(x-a)Q(x)+(x-a)²Q'(x) [Product rule]

When you sub in x=a
P'(a)=0 hence proven true

Hope that helped

 

[star*eyed]

got it now thanx!