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Find t if the expansion of the product of x^3 - 4x^2 + 2x - 5 and x^2 + tx - 7 has no x^2 term.

 Feb 19, 2019
 #1
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x^3 - 4x^2 + 2x - 5 and x^2 + tx - 7

 

So  we have

 

(x^3 - 4x^2 + 2x - 5)  (x^2 + tx - 7 )   =

 

    x^5 - 4x^4 + 2x^3 - 5x^2

          + tx^4 - 4tx^3 +2tx^2  - 5tx

                    -7x^3  + 28x^2  - 14x  + 35

 

If we have no x^2 term   this means  that

 

( - 5 + 2t + 28)x^2   =   0x^2

 

Which implies that

 

-5 + 2t + 28 = 0

 

23 + 2t = 0

 

2t = -23        divide both sides by  2

 

t = -23/2

 

 

cool cool cool

 Feb 19, 2019

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