Solve for p, q, and r in 2x^2 − 12x + p = q(x − r)^2 + 10 for all x values

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Homework Help Overview

The discussion revolves around solving the equation 2x^2 − 12x + p = q(x − r)^2 + 10 for the variables p, q, and r. Participants are exploring the relationships between these variables and their values based on the polynomial identity.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equivalence of polynomial expressions and the method of comparing coefficients. There is an attempt to express the left side in a different form and questions arise regarding the correctness of the transformations made.

Discussion Status

Some participants have provided insights into the process of comparing coefficients, while others have expressed confusion over the transformations and the values of p, q, and r. There is a mix of interpretations regarding the polynomial forms, and some participants indicate they have resolved their understanding.

Contextual Notes

There appears to be some disagreement on the values of p, q, and r, with different interpretations of the polynomial forms leading to varying conclusions. The discussion reflects an ongoing exploration of the problem without a definitive consensus on the correct values.

DeanBH
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2x^2 − 12x + p = q(x − r)^2 + 10 for all values of x find p q and r

i've got

2(x-3)^2 + p = Q(x-r)^2 + 10

so q = 2 r = 3 and p = 10?

now the answers say that Q = 2 r = 3 and p = 28?

can someone explain how to properly go about doing this equation.
 
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2x^2 − 12x is not the same as 2(x-3)^2
 
If a polynomial equation is true for all values of x, then "corresponding coefficients"- that is, coefficients multiplying the same powers of x on opposite sides of the equation- must be the same: multiply the square on the right and compare "corresponding coefficients".
 
kamerling said:
2x^2 − 12x is not the same as 2(x-3)^2



k I've done it now, thx
 

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