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.
+128475 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
