SOLUTION: got stuck with this one please help find the value of A,B and C that ensure the two polynomials y1(x)=-4x^2+9x-10 and y2(x)=A(x+10)+B(x-5)+C(x^2-4x-9) are equal for all values o

Algebra ->  Functions -> SOLUTION: got stuck with this one please help find the value of A,B and C that ensure the two polynomials y1(x)=-4x^2+9x-10 and y2(x)=A(x+10)+B(x-5)+C(x^2-4x-9) are equal for all values o      Log On


   

Question 873564: got stuck with this one please help
find the value of A,B and C that ensure the two polynomials y1(x)=-4x^2+9x-10 and y2(x)=A(x+10)+B(x-5)+C(x^2-4x-9) are equal for all values of x.


thanks so much for your help in advance
Matt
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify y2 equation and put into general form, decreasing powers of x; and then equate corresponding coefficients. You will have three equations in the unknowns, A, B, and C.
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Skipping the steps here, but done separately on paper, the y2 expression becomes
Cx%5E2%2BAx%2BBx-4Cx%2B10A-5B-9C
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Are you still stuck?
"yes".

Simplifying the y2 equation's right side:
Ax%2B10A%2BBx-5B%2BCx%5E2-4Cx-9C
Cx%5E2%2BAx%2BBx-4Cx%2B10A-5B-9C
Cx%5E2%2B%28A%2BB-4C%29x%2B%2810A-5B-9C%29

Now as given y1 equation to be equal to y2 eqation,
-4x%5E2%2B9x-10=Cx%5E2%2B%28A%2BB-4C%29x%2B%2810A-5B-9C%29
The coefficients in corresponding positions are equal. This gives a system,
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-4=C
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9=A+B-4C
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-10=10A-5B-9C

Solve that system for A, B, and C.