+108 The roots of x^3-6x*^2-13x-k=0 form an artithmetic sequence.
a) What is the median term of the arithmetic sequence
b) Find the value of k
+129850 Call the roots a , a + d and a + 2d
Sum of the roots = 6
Sum of product of the roots taken two at a time = -13
So we have this system
a + a + d + a + 2d = 6
a(a + d) + a (a + 2d) + (a + d) ( a + 2d) = -13
A little tedious to solve this....so...I'm leaning on WolframAlpha ( I can go through it if you want me to)
We have two possible arithmetic sequences
First one
a = -3 d = 5
So
-3 , 2 , 7 are the roots
So
( x + 3) ( x - 2) ( x - 7) = x^3 - 6 x^2 - 13 x + 42 so k = - 42
Second one
a = 7 d = -5
So again
7 , 2 , -3 are the roots and we get the same value for k
And the median term = 2
