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Roots of a cubic equation

If a,b and c are the roots of the equation x^3-5x+3=0 find the value of a^2+b^2+c^2

I got 10 , the book got -10

And another one.
If a,b and c are the roots of the equation x^3+x^2+4x-5=0 find the cubic equation whose roots are ab, ac and bc.

I got x^3-4x^2-5x-25=0 and the book got x^3-4x^2-4x-25=0 . Any help please?

Reply 2

Lukedavidhopkins1

Original post by Farhan.Hanif93

The book is right.

(a+b+c)^2 - 2(ab+bc+ca) =a^2+b^2+c^2

But the equation for ab+bc+ac is c/a which in this case is -5 as -5/1 =-5 and that times -2 is +10 right? Because there's not a x^2 term :/ so confused -.-

Reply 3

Farhan.Hanif93

Original post by Lukedavidhopkins1

But the equation for ab+bc+ac is c/a which in this case is -5 as -5/1 =-5 and that times -2 is +10 right? Because there's not a x^2 term :/ so confused -.-

Oops, yes you're right.

Reply 4

Lukedavidhopkins1

Original post by Farhan.Hanif93

Oops, yes you're right.

Thanks

what about my second question?

EDIT just realised how arrogant that smiley could look with the way it's eyes are :/

Reply 5

Farhan.Hanif93

Original post by Lukedavidhopkins1

Thanks

what about my second question?

EDIT just realised how arrogant that smiley could look with the way it's eyes are :/

I agree with your answer.

Reply 6

Lukedavidhopkins1

Original post by Farhan.Hanif93

I agree with your answer.

Thanks for checking it for me :smile:

just wasn't sure whether I was screwing up or it was a printing error

Reply 7

Phenomenological

Erm, unless you're going into complex numbers somewhere how can the sum of three squares be negative? Just based on that the book is clearly wrong.

Reply 8

Lukedavidhopkins1

Original post by Phenomenological

Erm, unless you're going into complex numbers somewhere how can the sum of three squares be negative? Just based on that the book is clearly wrong.

Well I put it as a positive 10 so the book must be wrong with -10 then as you've just pointed out as this equation isn't asking for complex roots

Reply 9

RichE

Original post by Phenomenological

Erm, unless you're going into complex numbers somewhere how can the sum of three squares be negative? Just based on that the book is clearly wrong.

Without doing a little further analysis it's not terribly clear whether that cubic has complex roots or not (as it happens it hasn't).

Reply 10

Phenomenological

Original post by RichE

Without doing a little further analysis it's not terribly clear whether that cubic has complex roots or not (as it happens it hasn't).

I made an assumption based on the question, it hardly looked like particularly complex material.

That was inadvertent, but I'll get my coat regardless. :tongue: