Math Is Fun Forum

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Irrational Roots Questions

1) Let f(x) = x^3+bx+c, where b and c are integers.

If f(5+\sqrt 3)=0, determine b+c.

I know that 5-\sqrt 3 is also a root, but how to continue?
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2) Find a monic quartic polynomial f(x) with rational coefficients whose roots include

. Give your answer in expanded form.

???
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3) Suppose $P(x)$ is a polynomial of smallest possible degree such that:

-P(x) has rational coefficients

-P(-3) = P(\sqrt 7) = P(1-\sqrt 6) = 0

-P(-1) = 8

Determine the value of P(0).

???

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Irrational Roots Questions

Hi;

For 1)
Plugin the two irrational roots and determine b and c.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Irrational Roots Questions

I can only give hints. My hands are bound.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}