+0  
 
+1
32
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avatar+151 

Consider the polynomial P(x) = x^4 + 3x^3 + 5x^2 + 7x + 9. Let its four roots be a, b, c, d. Evaluate the expression (a + b + c)(a + b + d)(a + c + d)(b + c + d).

 Oct 10, 2020
 #1
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0

The roots of x^4 + 3x^3 + 5x^2 + 7x + 9 are

-1.6673 - 0.9330*i

-1.6673 + 0.9330*i

0.1673 - 1.5613*i

0.1673 + 1.5613*i

 

Plugging these into (a + b + c)(a + b + d)(a + c + d)(b + c + d), we get -12.

 Oct 10, 2020
 #2
avatar+31093 
+1

I get the following:

 

Guest #1 has correctly identified the roots (approximately), but I think he/she has made a mistake in the final multiplication. 

 Oct 10, 2020

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