SOLUTION: hello there wonderful tutor, i am in need of your fine assistance, if you would be so kind! this problem has been rattling my brain---please save me!!! here it is..... A

Question 244371: hello there wonderful tutor, i am in need of your fine assistance, if you would be so kind! this problem has been rattling my brain---please save me!!! here it is.....
A polynomial equation for the variable x and of the smallest degree with rational coefficients has one root of: sqrt(3)+ sqrt(2) all over sqrt(3)-sqrt(2)... and a second root of: sqrt(11)+sqrt(10) all over sqrt(11)-sqrt(10)..... If the coefficient of the x term in the polynomial equation is -52, find the coefficient of the x^2 term.
(i just added the colons and dot dot dots for organization)
ok, PLEASE help!!!!!!!!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
"one root of: sqrt(3)+ sqrt(2) all over sqrt(3)-sqrt(2)"
___ multiplying numerator and denominator by [sqrt(3)+ sqrt(2)] ___ 5 + 2 sqrt(6)
___ conjugate root ___ 5 - 2 sqrt(6)
___ resulting factor [(x - R1)(x - C1)] ___ x^2 - 10x + 1

"second root of: sqrt(11)+sqrt(10) all over sqrt(11)-sqrt(10)"
___ multiplying numerator and denominator by [sqrt(11)+ sqrt(10)] ___ 21 + 2 sqrt(110)
___ conjugate root ___ 21 - 2 sqrt(110)
___ resulting factor [(x - R2)(x - C2)] ___ x^2 - 42x + 1

multiplying the factors ___ x^4 - 52x^3 + 422x^2 - 52x + 1
RELATED QUESTIONS
Hello, can I so kindly ask for assistance with the problem below: Fill in the tables... (answered by checkley71)

My niece is being home-schooled (8th grade) and has gotten into some algebra and geometry (answered by Targetweek,rapaljer)

Hello tutor, I would really appreciate it if you helped me with this problem. Complete (answered by Fombitz)

Salutations to all of you wonderful tutors who have wonderful math genes and don't mind (answered by stanbon)

Hello, I am trying to help a young man out with his home work. Apparently it has been (answered by checkley77,richwmiller)

WE NEED HELP!! Hello my 10 year old son has a word problem on his math worksheet and I... (answered by scott8148)

I am kind of confused on this so if anyone out there can help in any way it would be... (answered by solver91311)

Hello, My Name is Donna and I must say, I am so pleased you have the ratings in the... (answered by dragonwalker)

I have been asked to find the z-score for a normal distribution that has a mean of 100... (answered by MathTherapy)