Polynomials question (1 Viewer)

[whitnall8]

Could someone please help me with this question:

If ax^3 + cx + d has a double root, show that 27da^2 + 4b^3 = 0

 

[scardizzle]

your question isn't making much sense to me. Where did you get the b term from? The only advice i can give atm is this q probably involves differentiating and making x the subject

 

[khorne]

y' => 3ax^2 + c = 0

=> x = +/- sqrt(-c/3a)

sub it in, divide through by sqrt(-c/3a), and re-arrange, square, collect like terms, and you will have it.

 

[whitnall8]

Sorry, I was caught between two questions.

The actual question is:

If ax^3 + cx + d has a double root, show that 27ad^2 + 4c^3 = 0

 

[Sakeeee]

Sorry, I was caught between two questions.

The actual question is:

If ax^3 + cx + d has a double root, show that 27ad^2 + 4c^3 = 0

sub @ as a root

a@^3+c@x+d=0 eqn(1)

now lets find what @ equals to

y'=3ax^2+c

x^2=-c/3a

that means @^2=-c/3a since @ is the root

sub it into eqn 1
a(-c/3a)^(3/2) + c(-c/3a)^(1/2)+d=0

[(-c/3)^3/2]/a^(1/2) + [(-c)^(3/2)]/3a)+d=0

Yeah it's getting hard to simply with this inefficient forum. you do the rest it will work

 

[cutemouse]

This is from a CSSA trial. It comes up now and then