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# polynomials

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

Apr 11, 2021

#1
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(x3 - 4x2 + 5x - 5)(x2 + tx - 7)
Find the pairs that make x2 terms:
(-4x2)(-7) + (5x)(tx) + (-5)(x2)
= 28x2 + 5tx2 - 5x2

= 23x2 + 5tx2

Since you're trying to find no x2 term:

23x2 + 5tx2 = 0

23 + 5t = 0

5t = -23

t = $$-\frac{23}{5}$$   or   -4.6

Apr 11, 2021