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# Functions Problem

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Given that f(x)=5x^2 - 3x + 7 and f(g(x)) = 40 - 11x^2 - 8x^4, find all possible values for the sum of the coefficients in the polynomial function g(x). Thank you to anyone who replies :)

Sep 11, 2018

### 3+0 Answers

#1
+27908
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Are you sure you have written the equations correctly?  g(x) must be of order 2, so its highest order term is ax2. This means we must have 5a2 = -8   (because 5a2x4 must equal -8x4).  This would make 'a' an imaginary number!

Sep 12, 2018
#2
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Hi Alan. Yes, I am sure I wrtoe the question correctly.

Sep 12, 2018
#3
+101745
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Alan is right, the leading coefficient of g(x) must be     $$\sqrt{\frac{8}{5}}\;\;i$$

We both think that there is a mistake in the question.

Sep 13, 2018