Math Is Fun Forum

ABC1234

Member

Registered: 2016-12-22

Posts: 20

Intermediate Algebra

Please help on following:

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

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.}

ABC1234

Member

Registered: 2016-12-22

Posts: 20

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!
2) I'm not sure about this problem though.  All I know so far is that for

, we can turn it into

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Intermediate Algebra

That's a good start. Now, what is

? And

?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

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.}

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Intermediate Algebra

I get that too.

ABC1234

Member

Registered: 2016-12-22

Posts: 20

Re: Intermediate Algebra

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

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

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)

ABC1234

Member

Registered: 2016-12-22

Posts: 20

Re: Intermediate Algebra

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

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Intermediate Algebra

You only need the coefficients of

and

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