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the roots of x^3-6x^2-13x-k=0 form an arethmatic sequence

 

a) What is the median term of the arethematic sequence

b) Find the value of k

 Feb 15, 2021
 #1
avatar+113739 
+2

Let the sequence be      a-d,  a,  a+d

 

So 

 

\(x^3-6x^2-13x-k=(x-(a-d))\;x\;(x-(a+d))\\ x^3-6x^2-13x-k=x\;((x-a)+d))\;(x-a)-d))\\ x^3-6x^2-13x-k=x\;((x-a)^2-d^2)\\ etc\)

 

Simplify it down and equaet coefficients.

 Feb 15, 2021

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