anonymous
  • anonymous
One of the factors of (3x^2 −16x + k) is (x − 7). Determine the value of k.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
1. You know that the second expression that multiplies '(x-7)' must have a 3x because if it didn't you would not be able to obtain 3x^2 therefore,
anonymous
  • anonymous
\[(x-7)(3x+n)= 3x^2+xn-21x-7n\]
anonymous
  • anonymous
Now the original equation was \[3x^2-16x+k\] now setting that equal to the new equation, \[3x^2+xn-21x-7n=3x^2-16x+k \rightarrow xn-21x = -16x \rightarrow n = 5\] since n = 5 \[-7n \rightarrow -7(5) = -35\] , k = -35

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hartnn
  • hartnn
if x-7 is a factor, then x =7 is one of the root of the equation 3x^2 −16x + k = 0 ! so, x= 7 satisfies that equation. just plug in x=7 in that and find k :)
anonymous
  • anonymous
Refer to the attachment from Mathematica 9.
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