Math Is Fun Forum

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Algebraic Identity

Here is an identity

c and d are integers.

work out all possible pairs of values of (c) and (d). You must show your working.

(3x + c)(x + c) ≡ 3x^2 - dx + 16

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Algebraic Identity

hi PatternMan,

Set them equal:

For these to be equivalent for all x, the coefficients of x^2, of x, and of x^0 must each be equal.

So

and

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Re: Algebraic Identity

c^2 = 16.   - 4, or  4

4c = -d

when c  = 4

4(4), -d = 16, d = -16

when c = -4, d =  16

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Algebraic Identity

Yes. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

PatternMan

Member

Registered: 2014-03-08

Posts: 199

Re: Algebraic Identity

Yes. 

Bob

Gracias. I should have been able to get this one but I wasn't sure what the coefficient was for 4xc & -dx

Last edited by PatternMan (2014-04-01 10:31:46)

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"School conditions you to reject your own judgement and experiences. The facts are in the textbook. Memorize and follow the rules. What they don't tell you is the people that discovered the facts and wrote the textbooks are people like you and me."