Question

Consider the polynomial x^5+ax^4+bx^3+cx^2+dx+4 , where a,c,b,d are real numbers. If (1+2i) and (3-2i) are two roots of this polynomial then the value of a is :-

a)-524/65
b)-1/65
c)1/65
d)524/65

Answer 1

http://gamutech.com/chat/

Answer 2

openstudy is going don, you won't be getting answers for much longer, you'll have a better time over at http://gamutech.com/chat/

Answer 3

these complex roots always exist in conjugate pairs so 4 roots of the equation will be

(1 + 2i), (1 - 2i), (3 - 2i) and ( 3 + 2i)

Answer 4

the fifth root will be real

Answer 5

ok , then how to proceed ?

Answer 6

@gamootech m getting error to acces tht

Answer 7

you'd have to make an account, silly.
Openstudy is about to go down. Don't lose hope, I, and countless other helpers will be available over on http://gamutech.com/register/

Answer 8

it would be a pity of OS does go down..

Answer 9

LOL m trying to signup through fb, but it's showing tht the site is under construction dude

Answer 10

i tried out sum and product of roots formula but the ans is not matching, it's coming -516/65

Answer 11

sum and product of roots formula for an equation in x^5?

Answer 12

frm here http://en.wikipedia.org/wiki/Vieta's_formulas

Answer 13

oh ok I've only seen formulae for quadratics and cubics before.
unfortunately I gotta go now

Answer 14

good luck!

Answer 15

thanks

Answer 16

the quadratics which have the complex roots given in the equation are
x^2 - 2x + 5 and x^2 - 6x + 13 ( i was wrong the first time) - these are 2 factors of the function
when we multiply these it gives 65 as the last term
the original equation ended in + 4 so the third factor must be ( x + 4/65)

Answer 17

now if we expand this we get

(x^4 - 8x^3 + 25x^2 - 56x + 65)( x + 4/65)

= x^5 + 4x^4 / 65 - 8x^4 - and that's all the terms in x^4

so a = 4/65 - 8 = 4/65 - 520 / 65 = -516/65

I think you have the right answer