Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Proof of Some Quadratic Functions

So, I found these statements and I need your assistance to prove them since my body condition is not fit enough to think that much.
1. The quadratic equation whose roots are k less than the roots of

is

.
2. The quadratic equation whose roots are k more than the roots of

is

.
3. The quadratic equation whose roots are n times the roots of

is

.
4. The quadratic equation whose roots are negations of the roots of

is

.
5. The quadratic equation whose roots are inverses of the roots of

is

.
6. The quadratic equation whose roots are squareroots of the roots of

is

.
Thanks for your help.

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: [ASK] Proof of Some Quadratic Functions

Hi Monox D. I-Fly, I hope you recover soon. The proofs are very simple just use the quadratic formula as follows:

which proves (1)

which proves (2)

which proves (3)

which proves (4)

which proves (5). Finally we have:

but we have:

Therefore the last statement is correct only when a=b=c=1, otherwise there are something wrong with its proclaims. I hope that answers your question.

Last edited by Grantingriver (2019-04-08 00:32:42)

Alg Num Theory

Member

Registered: 2017-11-24

Posts: 693

Website

Re: [ASK] Proof of Some Quadratic Functions

6. The quadratic equation whose roots are squares of the roots of

is

x

.

https://mathhelpboards.com/pre-algebra- … post115152

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Me, or the ugly man, whatever (3,3,6)

Grantingriver

Member

Registered: 2016-02-01

Posts: 129

Re: [ASK] Proof of Some Quadratic Functions

Thank you Alg Num Theory, The corrected last statement can be proved as follows:

which completes the proofs. The link which Alg Num Theory has provided contains another correct proof of the theorem, if you would like.

Last edited by Grantingriver (2019-04-08 08:31:57)

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Proof of Some Quadratic Functions

Thank you, Grantingriver! Didn't expect that they are easier to understand than they look.

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.