Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

#1 2016-12-23 09:52:01

ABC1234
Member
Registered: 2016-12-22
Posts: 7

Intermediate Algebra

1) Suppose r and s are the values of x that satisfy the equation

for some real number m. Find the minimum real value of
.
Using vieta's I used the coefficients of the quadratic to express
as
, but I don't know what to do after that.

2) Let

and let
be the roots of f(x).  Compute
.

Thank you

Offline

#2 2016-12-23 18:54:08

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,115

Re: Intermediate Algebra

Hi dazzle1230;

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.

Online

#3 2016-12-24 02:57:40

Member
Registered: 2016-04-16
Posts: 982

Re: Intermediate Algebra

{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.}

Offline

#4 2016-12-24 07:54:27

ABC1234
Member
Registered: 2016-12-22
Posts: 7

Re: Intermediate Algebra

1) I got -8 too after completing the square: 2m^2-4m-6 -> 2(m^2-2m-3) -> 2((x-1)^2-4).  Thanks!

, we can turn it into

Offline

#5 2016-12-24 08:00:49

zetafunc
Member
Registered: 2014-05-21
Posts: 1,713
Website

Re: Intermediate Algebra

That's a good start. Now, what is
? And
?

Offline

#6 2016-12-24 16:21:23

Member
Registered: 2016-04-16
Posts: 982

Re: Intermediate Algebra

{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.}

Offline

#7 2016-12-24 23:16:54

zetafunc
Member
Registered: 2014-05-21
Posts: 1,713
Website

I get that too.

Offline

#8 2016-12-25 08:00:11

ABC1234
Member
Registered: 2016-12-22
Posts: 7

Re: Intermediate Algebra

I see after using substitution but what about -4x+3?

Offline

#9 2016-12-25 08:56:03

zetafunc
Member
Registered: 2014-05-21
Posts: 1,713
Website

Re: Intermediate Algebra

How can you relate the sum of the roots of a polynomial to its coefficients?

Last edited by zetafunc (2016-12-25 08:56:13)

Offline

#10 2016-12-27 04:14:08

ABC1234
Member
Registered: 2016-12-22
Posts: 7

Re: Intermediate Algebra

I know how to find the sum of roots using vieta's, but how am I supposed to find the coefficients?

Offline

#11 2016-12-27 04:50:12

zetafunc
Member
Registered: 2014-05-21
Posts: 1,713
Website

Re: Intermediate Algebra

You only need the coefficients of
and

Last edited by zetafunc (2016-12-27 04:50:38)

Offline